 # 1. Winning Strategy In a game show like the one described in Example I, a prize is con-cealed behind one of ten doors. After the contestant chooses a door, the host opens eight los-ing doors and then gives the contestant the opportunity to switch to the other unopened door. (a) Play this game with a friend 30 or more times. using the strategy of switching doors each time. Count the number of times you win, and estimate the probability of winning with this strategy. ( b) Calculate the probability of winning with the switching strategy using reasoning similar to that in Example I. Compare with your result from part (a). ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
Publisher: Cengage Learning
ISBN: 9781305071742 ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
Publisher: Cengage Learning
ISBN: 9781305071742

#### Solutions

Chapter
Section
Chapter 14.FOM, Problem 1P
Textbook Problem

## 1. Winning Strategy In a game show like the one described in Example I, a prize is con-cealed behind one of ten doors. After the contestant chooses a door, the host opens eight los-ing doors and then gives the contestant the opportunity to switch to the other unopened door.(a) Play this game with a friend 30 or more times. using the strategy of switching doors each time. Count the number of times you win, and estimate the probability of winning with this strategy. (b) Calculate the probability of winning with the switching strategy using reasoning similar to that in Example I. Compare with your result from part (a).

Expert Solution
To determine

a)

To find:

The probability of winning by using the strategy.

Solution:

The probability of winning by using the strategy is 0.1.

### Explanation of Solution

Approach:

The formula of probability of an event is given by,

P(E)=n(E)n(S)

Here, n(E) is the number of favorable outcomes for event E and n(S) is the number of total possible outcomes.

Calculation:

The game was played 30 times so possible chances of winning is 30.

n(S)=30

The number of times person won is 3.

n(E)=3

Substitute 30 for n(S) and 3 for n(E) in above mentioned formula of probability.

P(E)=330=110=0.1

Conclusion:

Hence, the probability of winning by using the strategy is 0.1.

Expert Solution
To determine

b)

To find:

The probability of winning by using the switching strategy.

Solution:

The probability of winning by using the switching strategy is 0.9.

### Explanation of Solution

Approach:

The formula of probability of an event is given by,

P(E)=n(E)n(S)

Here, n(E) is the number of favorable outcomes for event E and n(S) is the number of total possible outcomes.

The formula for the complement of E is P(E)=1P(E)(1)

Calculation:

From part (a), P(E)=0.1.

If the contestant decides to switch, she will switch to the winning door if she had initially chosen a losing one and vice-versa.

Substitute 0.1 for P(E) in equation (1).

P(E)=10.1=0.9

Conclusion:

Hence, the probability of winning by using the switching strategy is 0.9.

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