Question

A baseball player has a batting average of 0.33. What is the probability that he has exactly 4 hits in his next 7 atbats? Round to 3 decimal places.The probability is

Answer 1

Given that the player can or cannot hit the ball, then this situation can be modeled with the binomial distribution.

Binomial distribution formula

`P=_nC_xp^x(1-p)^(n-x)^{}`

where

• P: binomial probability

,

• nCx: number of combinations

,

• p: probability of success in a single trial

,

• x: number of times for a specific outcome within n trials

,

• n: number of trials

Substituting with n = 7, x = 4, and p = 0.33, we get:

`\begin{gathered} P=_7C_4(0.33)^4(1-0.33)^(7-4) \\ P=35(0.33)^4(0.67)^3 \\ P\approx0.125 \end{gathered}`

The probability is 0.125