Chapter 11, Problem 5CR

To determine

To conclude: about the prize when it is behind Door A for 32 out of 50 contestants

Answer to Problem 5CR

Because this result is obtained more than half of the time, it is concluded the host's claim is most likely false.

Explanation of Solution

Given:

Prize is behind Door A for 32 out of 50 contestants

Calculation:

Given that the prize on a game show is placed behind either Door A or Door B. If have to tell that what will be the conclusion when the prize is behind Door A for 32 out of 50 contestants.

Since there are two choices only Door A and Door B. therefore probability of randomly choosing any one door is 0.5.

Getting 32 out of 50 contestants with the prize behind Door A corresponds to a proportion of $\frac{32}{50}=0.64$ .

This is higher than a probability of 0.5.

Because this result is obtained more than half of the time, it is concluded the host's claim is most likely false.

Conclusion:

Because this result is obtained more than half of the time, it is concluded the host's claim is most likely false.