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Chapter 8: Problem 47

A soccer player is more likely to score on his second shot if he was successful on his first. Can we model a succession of shots a player takes as a sequence of Bernoulli trials? Explain.

Short Answer

Expert verified
No, we cannot model the succession of shots as a sequence of Bernoulli trials because the outcomes of the shots are not independent as the probability of scoring on the second shot is affected by the outcome of the first shot.

Step by step solution

01

Definition of Bernoulli Trials

A Bernoulli trial consists of a random experiment with two possible outcomes鈥攕uccess or failure鈥攁nd the probability of success remains constant throughout the trials. Additionally, the trials should be independent, meaning the outcome of one trial should not affect the outcome of any other trials.
02

Analyzing the Soccer Player's Shots

According to the given information, the probability that a soccer player scores on his second shot is affected by whether or not he scored on his first shot. This suggests that the outcomes of the two shots are not independent.
03

Conclusion

Since the outcomes of the soccer player's shots appear to be dependent on each other, we cannot model the succession of shots as a sequence of Bernoulli trials.

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