Focus on the ‘Big Wheel’ problem from the Price is Right. With knowing how to calculate whether or not the final contestant will win. Here, we are going to examine the probabilities of how they will lose rather than whether or not they lose. There are three ways to lose: (1) after two spins, there is a tie between the final contestant and the best amount and the final contestant loses the spin-off, (2) after two spins, the final contestant’s total is greater than $1 and (3) after two spins, the final contestant’s total is less than the best current amount. For these calculations, we will focus on the situation where the current best amount is $1 (i.e., the only way for the final contestant to win is to tie and then win in a spin-off). (a) Determine the probability that the final contestant has tied the $1 amount and subsequently loses in the spin-off (where we assume each contestant has a 50% chance of winning the spin-off). Important Note: You must consider both tie-ing after 1 spin and also tie-ing after two spins. (b) For each first initial spin from s = .05, .10, .15, . . . , .95, determine P(final contestant’s total after 2 spins > $1|first spin = s). Hint: You may want to organize your calculations in a systematic way. (c) Given your solution to (b), determine the probability that after two spins the final contestant’s total is greater than $1. (d) For each first initial spin from s = .05, .10, .15, . . . , .95, determine P(final contestant’s total after 2 spins < $1|first spin = s). Hint: If you are careful, you can use the answer to (b) to help. (e) Given your solution to (d), determine the probability that after two spins the final contestant’s total is less than $1.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Please do this with hand written work and do all parts please Focus on the ‘Big Wheel’ problem from the Price is Right. With knowing how to calculate whether or not the final contestant will win. Here, we are going to examine the probabilities of how they will lose rather than whether or not they lose. There are three ways to lose: (1) after two spins, there is a tie between the final contestant and the best amount and the final contestant loses the spin-off, (2) after two spins, the final contestant’s total is greater than $1 and (3) after two spins, the final contestant’s total is less than the best current amount. For these calculations, we will focus on the situation where the current best amount is $1 (i.e., the only way for the final contestant to win is to tie and then win in a spin-off). (a) Determine the probability that the final contestant has tied the $1 amount and subsequently loses in the spin-off (where we assume each contestant has a 50% chance of winning the spin-off). Important Note: You must consider both tie-ing after 1 spin and also tie-ing after two spins. (b) For each first initial spin from s = .05, .10, .15, . . . , .95, determine P(final contestant’s total after 2 spins > $1|first spin = s). Hint: You may want to organize your calculations in a systematic way. (c) Given your solution to (b), determine the probability that after two spins the final contestant’s total is greater than $1. (d) For each first initial spin from s = .05, .10, .15, . . . , .95, determine P(final contestant’s total after 2 spins < $1|first spin = s). Hint: If you are careful, you can use the answer to (b) to help. (e) Given your solution to (d), determine the probability that after two spins the final contestant’s total is less than $1.

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