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# The Monty Hall Problem

Some months ago, I had the honor of interviewing Monty Hall for a story I was writing. If you don't know, Monty created and hosted one of TV's longest-running game shows, Let's Make a Deal. (non sequitur: I'm once again reminded of that hilarious exchange in Airplane II: Lloyd Bridges's character: "If anyone has any ideas - anything at all - now is the time to speak up." Jacob: "How about a game show like Hollywood Squares, but with kids? Gary Coleman could host.")

So Monty Hall. He was one of those figures I remember from growing up "“ always on TV, someone you could trust to make you smile, an affable host with a pretty interesting game show in his command. The interview went fantastically well, and I learned a lot about not only the origins of the show (the network pulled the plug after seeing the pilot, but later threw it on the schedule as a last-minute replacement for another show that had bombed), but Mr. Hall, too.
What I didn't know when I was a kid growing up watching the show, but only discovered in doing research for the interview, was something known as the "Monty Hall Paradox." (AKA "Monty Hall Problem") In a nutshell, the paradox asks the question: Do the player's chances of getting the car (behind door number 1, 2, or 3) increase by switching doors once a guess has been made (so technically it's down to two doors at that point).

I'll post the answer after the jump, but I'd be interested to know what you think before you click through.

Interestingly, the answer is always YES. From Wiki:

Once the host has opened a door, the car must be behind one of the two remaining doors. The player has no way to know which of these doors is the winning door, leading many people to assume that each door has an equal probability and to conclude that switching does not matter (Mueser and Granberg, 1999). This "equal probability" assumption, while being intuitively seductive, is incorrect. The player's chances of winning the car actually double by switching to the door the host offers.

For a very complex answer to WHY this is so, check out the full Wiki article, including a discussion of Bayes' theorem. If any of you recall my post on Mark Haddon's novel, the curious incident of the dog in the night-time, and have read the novel, you'll also find a pretty cool discussion of the Monty Hall Problem there.

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On Saturday, September 23, museums and cultural institutions across the United States will open their doors to the public for free, as part of Smithsonian magazine’s annual Museum Day Live! event. Hundreds of museums are set to participate, ranging from world-famous institutions in major cities to tiny, local museums in small towns. While the full list of museums can be viewed, and tickets can be reserved, on the Smithsonian website, we’ve collected a small selection of the fantastic museums you can visit for free this Saturday.

#### 1. NEWSEUM // WASHINGTON, D.C.

The Newseum in Washington, D.C. is an entire museum dedicated to the First Amendment. Celebrating freedom of religion, speech, press, assembly and petition, the museum features exhibits on civil rights, the Berlin Wall, and the history of news media in America. Their latest special exhibitions take a look back at the event of September 11, 2001 and go inside the FBI's crime-fighting tactics.

#### 2. INTREPID SEA, AIR & SPACE MUSEUM // NEW YORK CITY, NEW YORK

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New York's Intrepid Sea, Air & Space Museum doesn’t just showcase America’s military and maritime history—it is a piece of that history. The museum itself is one of the Essex-class aircraft carriers built by the United States Navy during World War II. Visitors can explore its massive deck and interior, and view historic airplanes, a real World War II submarine, and a range of interactive exhibits. Normally, a ticket will set you back a whopping \$33 (or \$19 for New York City residents), but on Saturday, general admission is free with a Museum Day Live! ticket.

#### 3. AUTRY MUSEUM OF THE AMERICAN WEST // LOS ANGELES, CALIFORNIA

Perfect for art lovers, history buffs, and cinephiles alike, the Autry Museum of the American West (named for legendary singing cowboy Gene Autry) offers up an eclectic mix of art, historical artifacts from the real American West, and Western film memorabilia and props.

#### 4. MUSEUM OF ARTS AND SCIENCES // DAYTONA BEACH, FLORIDA

A massive art, science, and history museum located on a 90-acre nature preserve, the Museum of Arts and Sciences features the largest collection of Florida art anywhere in the world, as well as the largest collection of Coca-Cola memorabilia in all of Florida. Its diverse exhibits are alternately awe-inspiring, informative, and quirky, ranging from an exploration of 2000 years of sculpture art to an exhibition of 19th and 20th century advertising posters.

#### 5. INTERNATIONAL MUSEUM OF THE HORSE AT THE KENTUCKY HORSE PARK // LEXINGTON, KENTUCKY

The International Museum of the Horse explores the history of—you guessed it!—the horse. That might sound like a narrow scope, but the museum doesn’t just display horse racing artifacts or teach you about modern horse breeds. Instead, it endeavors to tackle the 50-million-year evolution of the horse and its relationship with humans from ancient times to modern times.

#### 6. THE PEGGY NOTEBAERT NATURE MUSEUM // CHICAGO, ILLINOIS

Pete LaMotte, Flickr // CC BY-NC-ND 2.0

The 160-year-old Peggy Notebaert Nature Museum is pulling out all the stops for this year’s Museum Day Live! In addition to their vast exhibits of animal specimens and cultural artifacts, the museum will be hosting a live animal feeding and a butterfly release throughout the day.

#### 7. OGDEN MUSEUM OF SOUTHERN ART // NEW ORLEANS, LOUISIANA

The Ogden Museum of Southern Art aims to teach visitors about the rich culture and diverse visual arts of the American South. Right now, visitors can view a collection of William Eggleston's photographs and check out the museum's 10th annual invitational exhibition of ceramic teacups and teapots.

#### 8. BALTIMORE MUSEUM OF INDUSTRY // BALTIMORE, MARYLAND

Marcin Wichary, Flickr // CC BY 2.0

Located in a 19th century oyster cannery on the Baltimore waterfront, the Baltimore Museum of Industry tells the story of American manufacturing from garment making to video game design. Visitors this weekend can meet video game designers and create custom games at the museum’s interactive “Video Game Wizards” exhibit.

#### 9. SYLVAN HEIGHTS BIRD PARK // SCOTLAND NECK, NORTH CAROLINA

You can meet 2000 birds from around the world this weekend at the 18-acre Sylvan Heights Bird Park. Visitors to the massive garden can walk through aviaries displaying birds from every continent except Antarctica, including ducks, geese, swans, and exotic birds from all over the world.

#### 10. DELTA BLUES MUSEUM // CLARKSDALE, MISSISSIPPI

Visit Mississippi, Flickr // CC BY-ND 2.0

Visitors to the Delta Blues Museum can learn about the unique American musical art form in “the land where blues began,” with audiovisual exhibits centered on blues and rock legend Don Nix, as well as Paramount Records illustrator Anthony Mostrom.

#### 11. NATIONAL MUSEUM OF NUCLEAR SCIENCE & HISTORY // ALBUQUERQUE, NEW MEXICO

America’s only congressionally chartered museum dedicated to the story of the Atomic Age, the National Museum of Nuclear Science & History features exhibits on everything from nuclear medicine to representations of atomic power in pop culture. Adult visitors to the museum will delight in its impressively nuanced take on nuclear technology, while kids will love the museum’s outdoor airplane exhibit and hands-on science activities at Little Albert’s Lab.

#### 12. MUSEUM OF THE MOUNTAIN MAN // PINEDALE, WYOMING

sporst, Flickr // CC BY 2.0

Dedicated to the mountain men who explored and settled Wyoming in the 19th century, the Museum of the Mountain Man brings American folklore and legends to life. The museum features exhibits on the Rocky Mountain fur trade and tells the story of American folk legend and famed mountain man Hugh Glass (the man Leonardo DiCaprio won an Oscar playing in 2015's The Revenant).

#### 13. BESH BA GOWAH ARCHAEOLOGICAL PARK AND MUSEUM // GLOBE, ARIZONA

Arizona’s Besh Ba Gowah Archaeological Park and Museum lets visitors connect with history firsthand. The museum is home to the ruins and artifacts of the Salado Indians who inhabited Arizona from the 13th century through the 15th century, and even lets visitors wander through an 800-year-old Salado pueblo.

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12 Secrets of Sephora Employees
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With more than 2000 stores in 33 countries, Sephora has arguably become the ultimate destination for all things beauty-related. Founded in France in 1970, the cosmetics giant sells a variety of makeup, nail polish, perfume, and skincare products, but it’s not your average beauty store. The shops offer customers an interactive experience, with beauty advice and free samples galore. We got the skinny on what it’s like to work there—from the special vocabulary they use to why they’re always happy to give out samples.

#### 1. THEY HAVE THEIR OWN LINGO.

Sephora employees use a variety of terms to refer to themselves, their wardrobe, and where they work. Employees who interact with customers on the sales floor (a.k.a. the stage) are dubbed cast members, and managers are called directors. Continuing the theatrical theme, Sephora employees refer to their uniforms as costumes and call the back area of the store the backstage. There's also a particular term they use to describe all the free loot they get—gratis.

#### 2. WEARING MAKEUP IS A JOB REQUIREMENT.

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Sephora employees sometimes jokingly refer to their costumes’ futuristic style—black dresses with red stripes or black separates with red accents—as Star Trek attire. But besides donning Trek-y garb, Sephora employees must also wear fragrance and a full face of makeup. “We had a minimum amount that we had to wear every day, and we got written up if we didn’t wear it,” writes Garnetstar28, a former color and fragrance expert at Sephora, on Reddit. “In the beginning it was fun, but when I started working the opening shift I really started to hate having to put that much makeup on at 6 in the morning."

While most employees must wear eyeliner, eye shadow, mascara, foundation, blush, and lipstick, some of them can get away with wearing less makeup, depending on their area of specialty and the location of the store. And although they don’t necessarily need to wear products sold at Sephora, management often encourages employees to do so because many customers ask cast members about the products they personally use.

#### 3. THEY MIGHT NEVER HAVE TO BUY THEIR OWN MAKEUP …

Reps from various beauty brands regularly visit Sephora stores to educate employees about their new products and how to use them. In these trainings, which typically occur a few times a week, Sephora workers may receive free products (in full, half, or sample sizes) to try. That can add up quickly, with some employees estimating that they’ve accumulated thousands of dollars worth of products. “I will most likely never have to buy mascara ever again,” writes Kaitierehh, a Sephora Color Lead (the manager of a store’s color cosmetics section), on Reddit.

#### 4. … BUT IF THEY DO, THEY GET HEFTY DISCOUNTS.

Mark Metcalfe/Getty Images

If Sephora employees want a specific product that’s missing from their gratis goodies, they can always purchase it from their employer—at a steep discount. Store policies vary, but most employees enjoy a 20 percent discount for in-store and online products. During the winter holidays, this discount increases to 30 percent, and products from Sephora’s own collection are always available for a 40 percent discount. Additionally, Sephora employees who work at stores inside J.C. Penney (Sephora has a partnership with the department store chain) enjoy a 20 to 30 percent discount on J.C. Penney products. Not a bad deal.

#### 5. THEY CAN WORK THEIR WAY UP FROM CASHIER TO SKINCARE PHD.

At Sephora, most new hires—who don’t need to have any makeup application experience—start at the bottom, working as cashiers or stocking the shelves overnight. But opportunities for growth abound. “Once you feel comfortable you can let your managers know you want ‘to go through build’ where you will learn about all the different ‘worlds’ the store has to offer,” a Sephora employee going by littleboots writes on Reddit. “Eventually you will be tested, and if you pass, you will have your very own brush belt.”

Sephora employees go through plenty of training, from the Science of Sephora (a curriculum covering makeup application and customer service) to hands-on learning from brand reps. “Sephora is amazing about education,” says Kim Carpluk, a Senior Artist and Class Facilitator at one of the company's New York City locations. “I’ve grown so much as an artist in just three years with the company,” she tells Mental Floss.

Cast members who complete additional training (beyond Science of Sephora) are eligible to earn a Skincare PhD, a senior title bestowed upon employees who have comprehensive knowledge and serve as personal beauty advisors to customers. Additionally, a select few become part of the Sephora Pro team, traveling the country to demonstrate makeup application techniques and represent the company on the brand’s social media channels.

#### 6. THEY WISH MORE PEOPLE WOULD PRACTICE GOOD HYGIENE.

Mark Metcalfe/Getty Images

The various testers around the store let customers dab on concealer, experiment with a new shade of gloss, or test a bold eye shadow. Although Sephora employees work hard to monitor and sanitize the testing stations, they can’t completely control what customers do. “I’ve seen people with cold sores, people with really nasty chapped lips, and people who were visibly sick using lipsticks and glosses on their mouths,” Garnetstar28 says. Besides the gross factor, contaminated makeup brushes, applicators, and wands can harbor bacteria (including E. coli) and spread infections. To minimize the risk, Sephora employees use alcohol-based sanitizers and encourage customers to use disposable applicators.

#### 7. THEY AREN’T PRESSURED TO MAKE COMMISSIONS.

Unlike salespeople at other beauty retailers, Sephora employees don’t work off commission—so they feel free to give customers their unbiased opinions about products. “We just really care. The reason a lot of us work for Sephora is because we don’t have to work off commission,” Carpluk says. “We’re there to support each other and make our clients feel beautiful and happy, and suggest what’s right for them based on their particular concerns.”

To encourage cast members to be positive and friendly (without the motivation of commissions), Sephora offers customers online surveys that allow them to rate their experience at a store. Managers may also reward cast members who meet hourly sales goals (selling more than \$100 worth of products in the next hour, for example) with free beauty products. “If we do extra well a manager might randomly let you choose extra gratis,” littleboots reveals.

#### 8. THEY'RE NOT ALL WOMEN.

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While many of Sephora’s employees (and customers) are women, you can still find plenty of men in the store. “I have three beautiful amazing super talented drag queens on my artistry team," Kaitierehh says. “At one of my previous stores, I even had two straight boys on my cast.” At Carpluk’s store in New York City, the employee ratio is almost 50/50 males to females. “We have a lot of men that work with us,” she says. “We even have a lot of male clients come in. I recently did a small makeover for an actor—I walked him through how to use foundation and concealer.”

#### 9. THEY’RE HAPPY TO GIVE YOU FREE SAMPLES …

Sephora is generous when it comes to free samples, and employees fully embrace the store’s bighearted policy. “I love to give out samples,” Carpluk says. “We’re there to help and to give out as many [samples] as possible. If you’re having trouble choosing between two foundations, we want you to take them home and try it out.” Typically, employees stick to giving three samples to each customer, but some are happy to give even more. “Anything we can squeeze into a container is the easiest—think foundation, primer, skin care,” littleboots says. “We can make a sad attempt to scrape out lip gloss or cut off a piece of lipstick too, it’s just not as effective.”

#### 10. … BUT THE STORE’S GENEROUS RETURN POLICY CAN IRRITATE THEM.

Joe Scarnici/Getty Images

Sephora’s return policy lets customers return anything (even "gently used" products) up to 60 days after buying it for a full refund, and customers who return items without a receipt get full store credit. While customers love the flexibility of trying products and returning them, some Sephora employees get frustrated when customers abuse the return policy. “I’ve seen entire articles written about how to take advantage of Sephora’s generous return policy by returning half used products and shades when the trends change and you get tired of them,” writes Ivy Boyd, who worked her way up at Sephora from a Product Consultant to Senior Education Consultant. “It infuriates me, to be honest, and is a very entitled attitude. When items are returned used, they are damaged out. They are destroyed. They go to complete waste.”

#### 11. THEY MIGHT NOT WEAR MAKEUP WHEN THEY’RE OFF THE CLOCK.

Sephora employees are passionate about makeup, but many of them choose to go barefaced on their days off. Besides saving time by skipping makeup, they can give their skin and pores much needed time to “breathe” without being smothered in products. Not all employees forego makeup on their days off, though. “Every single day of my entire existence I wear makeup,” Carpluk admits.

#### 12. THEY LOVE MAKING PEOPLE FEEL CONFIDENT.

Steve Jennings/Getty Images

Besides scoring free products and getting paid to work with makeup, Sephora employees love making people feel confident and beautiful. Whether they help a customer with acne find a good concealer or boost the self-confidence of someone with the right mascara, Sephora employees know the importance of self-image and the power of makeup to transform. “That’s actually why I feel happy going to work ever day,” Carpluk says. “A lot of women haven’t heard how beautiful their skin is, or how sparkly their eyes are, or that their lips are their best feature. I try to compliment my clients as much as possible throughout the service to let them know how gorgeous they are.”

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