Question

A football player has a 45% chance of getting a hit on any given pitch. What is the probability that the player earns a hit ignoring the balls before he strikes out (that requires four strikes)?

(a) 0.36

(b) 0.95

(c) 0.67

(d) 0.59

The question was posed to me in an interview for job.

This intriguing question comes from Geometric Probability topic in portion Discrete Probability of Discrete Mathematics

Answer 1

Right answer is (b) 0.95

The best explanation: IA success is a hit and a failure is a strike. The player requires either 0, 1, 2 or 3 failures in order to get a hit before striking out, so the probability of a hit is:

P(X=0) + P(X=1) + P(X=2) + P(X=3) = (0.45)^0(0.55) + (0.45)^1(0.55) + (0.45)^2(0.55) + (0.45)^3(0.55) = 0.95.