If a baseball player has a batting average of 0.420, what is the probability that the player will get at least 2 hits in the next four times at bat?
A) 0.333
B) 0.042
C) 0.50
D) 0.559

Question

Quizplus · Accepted Answer

The probability of getting at least 2 hits in the next four at-bats can be calculated by finding the complement of the probability of getting 0 or 1 hit. Let's denote the probability of getting a hit as p = 0.420 and the probability of not getting a hit as q = 1 - p = 0.580. The probabilities of getting exactly 0 or 1 hit are:- For 0 hits: $C(4,0) \cdot p^0 \cdot q^4 = 1 \cdot 1 \cdot 0.580^4$- For 1 hit: $C(4,1) \cdot p^1 \cdot q^3 = 4 \cdot 0.420 \cdot 0.580^3$The sum of these probabilities gives the probability of getting 0 or 1 hit. The complement of this sum gives the probability of getting at least 2 hits:$$P(\text{at least 2 hits}) = 1 - [P(\text{0 hits}) + P(\text{1 hit})]$$Calculating this gives a value greater than 0.5, which matches closest to option D, 0.559. This approach uses the binomial probability formula and the concept of complementary probability.

If a Baseball Player Has a Batting Average of 0