Question

The next four batters on a baseball team have hitting percentages of 0.400, 0.325, 0.250, and 0.300, respectively. The team currently has two outs. If any player gets an out, the next player or players will not get an opportunity to bat. What is the probability that the fourth player will have an opportunity to bat?
A) 0
B) 13/400

Answer 1

In order to the fourth player has the opportunity to bat, he/she needs that the three previous players make hit.


The joint probability of all three first batters make a hit is the product of their hitting percentages:


0.400 * 0.325 * 0.25


Pass the decimal numbers to fractions:


4/ 10 * 325/1000 * 25/100 = 32,500 / 1,000,000


Now simplify the fraction (divide numerator and denominator by 2500):


32,500 / 2,500 =   13

1,000,000 / 2,500 = 400


Then, 32,500 / 1,000,000 = 13 / 400


Answer: 13 / 400