Chapter 14.FOM, Problem 1P

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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

Explanation

**Approach:**

The formula of probability of an event is given by,

Here,

**Calculation:**

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

The number of times person won is

Substitute

**Conclusion:**

Hence, the probability of winning by using the strategy is

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

Explanation

**Approach:**

The formula of probability of an event is given by,

Here,

The formula for the complement of

**Calculation:**

From part

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

**Conclusion:**

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

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