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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
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).

To determine

a)

To find:

The probability of winning by using the strategy.

Answer

Solution:

The probability of winning by using the strategy is 0.1.

Explanation

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.

To determine

b)

To find:

The probability of winning by using the switching strategy.

Answer

Solution:

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

Explanation

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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Chapter 14 Solutions

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