“Let’s Make a Deal.” Marilyn vos Savant, who is listed in

Chapter 3, Problem 129SE

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QUESTION:

“Let’s Make a Deal.” Marilyn vos Savant, who is listed in Guinness Book of World Records Hall of Fame for “Highest IQ,” writes a weekly column in the Sunday newspaper supplement Parade Magazine. Her column, “Ask Marilyn,” is devoted to games of skill, puzzles, and mind bending riddles. In one issue (Parade Magazine, Feb. 24, 1991), vos Savant posed the following question:

Suppose you’re on a game show, and you’re given a choice of three doors. Behind one door is a car; behind the others, goats. You pick a door—say, #1—and the host, who knows what’s behind the doors, opens another door—say #3—which has a goat. He then says to you, “Do you want to pick door #2?” Is it to your advantage to switch your choice?

Marilyn’s answer: “Yes, you should switch. The first door has a 13 chance of winning [the car], but the second has a 23 chance [of winning the car].” Predictably, vos Savant’s surprising answer elicited thousands of critical letters, many of them from PhD mathematicians, who disagreed with her. Who is correct, the PhDs or Marilyn?

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QUESTION:

“Let’s Make a Deal.” Marilyn vos Savant, who is listed in Guinness Book of World Records Hall of Fame for “Highest IQ,” writes a weekly column in the Sunday newspaper supplement Parade Magazine. Her column, “Ask Marilyn,” is devoted to games of skill, puzzles, and mind bending riddles. In one issue (Parade Magazine, Feb. 24, 1991), vos Savant posed the following question:

Suppose you’re on a game show, and you’re given a choice of three doors. Behind one door is a car; behind the others, goats. You pick a door—say, #1—and the host, who knows what’s behind the doors, opens another door—say #3—which has a goat. He then says to you, “Do you want to pick door #2?” Is it to your advantage to switch your choice?

Marilyn’s answer: “Yes, you should switch. The first door has a 13 chance of winning [the car], but the second has a 23 chance [of winning the car].” Predictably, vos Savant’s surprising answer elicited thousands of critical letters, many of them from PhD mathematicians, who disagreed with her. Who is correct, the PhDs or Marilyn?

ANSWER:

Step 1 of 2

Since we have three doors ranked as #1, #2, and #3, the number of ways we can place a car (C) and 2 goats (G) behind the doors is 3.

Hence the sample space is,

   

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