Question

A baseball player has a batting average of 0.260. Suppose that you observe successive at-bats of the player and note for each at-bat whether the player gets a hit. For this player, successive trials at-bat are independent. What probability distribution will be used to calculate probability that the player will get two or more hits in his next four times at-bat?

Answer 1

Answer: Our required probability is 0.278.

Explanation:

Since we have given that

Probability that a player has a batting average = 0.260

Probability of success = 0.260

Probability of failure = 1-0.260 = 0.74

Number of times at bat = 4

Probability that the player will get two or more hits in his next four times at bat is given by

`P(X\geq 2)=P(X=2)+P(X=3)+P(X=4)\\\\P(X\geq 2)=^4C_2(0.26)^2(0.74)^2+^4C_3(0.26)^3(0.74+^4C_4(0.26)^4\\\\P(X\geq 2)=0.278`

Hence, our required probability is 0.278.