The Price Is Right: The Big Wheel

Probability Level 4

On the U.S. version of the gameshow The Price Is Right , three contestants have to encounter The Showcase Showdown in order to get into The Showcase . The game is played on a huge wheel dubbed The Big Wheel , which is filled with various point values in increments of fives from 5 5 all the way up to 100 100 . The winner is the one who gets the highest score on one or two spins. The last person has to get more point than the previous two, and it may result in a second spin whether he wants to do it or not. If he goes over 100 100 on the second spin, he will get eliminated by default. The overall score can be calculated as the score on one spin or the combined scores of two spins.

During a game of The Showcase Showdown , Alice and Brian have spun the wheel and each got the same overall score of 75 75 . What’s the possibility of Charles, the third player, winning this game without a tie? The possibility can be represented as a b \frac{a}{b} , submit your answer as a + b a + b .


The answer is 23.

Leah Jurgens by Leah Jurgens , 25, Vietnam

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1 solution

Leah Jurgens
Aug 11, 2019

There are 20 point values in the game.

In order for Charles to win this game without a tie, we have 2 cases:

  • Case 1: Charles gets over 75 right on one spin. In this case, he has to get 80 ; 85 ; 90 ; 95 ; 100 {80;85;90;95;100} , which is 5 point values. So the possibility in this case is:

P 1 = 5 20 = 1 4 P_1 = \frac{5}{20} = \frac{1}{4}

  • Case 2: Charles gets a a point value under or equal to 75 on the first spin, the possibility in this case is:

P 2 = 3 4 P_2 = \frac{3}{4} .

In order to win this game without a tie, Charles has to spin again to get combined scores of over 75, and at the same time, under or equal to 100. Therefore, he has to get 100 − a ; 95 − a ; 90 − a ; 85 − a ; 80 − a {100-a;95-a;90-a;85-a;80-a} on the second spin, which is 5 point values. The possibility in this case is:

P 3 = 5 20 = 1 4 P_3 = \frac{5}{20} = \frac{1}{4} .

Combining the two cases, the overall possibility of Charles winning this game is:

P = P 1 + P 2 ∗ P 3 = 7 16 P = P_1 + P_2 * P_3 = \boxed{\frac {7}{16}} .

1 Helpful 1 Interesting 0 Brilliant 0 Confused

I think there's a problem with this analysis; in case 2, Charles should not spin again if his first spin is exactly 75. See my report.

Patrick Corn - 1 year, 10 months ago

1 pending report

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