Question

Henry had a batting average of 0.341 last season (out of 1000 at-bats, he had 341 hits). Given that thisbatting average will stay the same this year, answer the following questions. What is the probability that his first hit will not occur until his 5th at-bat? Answers. 0.64. 0.083. 0.129. 0.166

Answer 1

The probability of success (a hit) is given by:

p = 0.341

The complement (a failure) of this probability is:

q = 1 - 0.341 = 0.659

Then, we can construct a probability distribution for the first hit until his nth at-bat:

`P(x=n)=p\cdot q^(n-1)`

For his 5th at-bat, we have n = 5, then:

`\begin{gathered} P(x=5)=0.341\cdot(0.659)^(5-1)=0.341\cdot0.659^4 \\ \\ \therefore P(x=5)=0.064 \end{gathered}`