Henry had a batting average of .0341.what is the probability that his first hit will not occur until his 5th at bat?

Question

Henry has a batting average of .341.  

What is the probability that his first hit will not occur until his 5th at bat?

What is the probability that his forst hit will occur within his first 5 at bats?

Of his next 20 at bats, what is the probability that he gets exactly 8 hits?

 

Answer 1

The first question is essentially asking for the probability that all of the first 4 at-bats are misses. In other words, the first four results are Fail, Fail, Fail, Fail. What's the probability of each of these individually? Then what is the probability of all 4 happening together?

 

The second question is related. Directly, the question: what is the probability in the first 5 bats, there is at least one success? An easier way to answer this is by looking at the complement, which would be NOT at least one success. In other words, what is the probability that all 5 are fails? If you find this result, then the answer to the question is just 1 minus that result.

 

The third question is more difficult to answer with a direct approach like the first two, but can be answered simply with the binomial formula.