# A player's batting average in softball is .400. What is the probability he gets 3 hits in his next 5 at-bats?

##### 1 Answer

The probability is exactly

#### Explanation:

This question calls for our old friend the Binomial distribution.

If we let

Why? Because the probability of a hit on a single at-bat is 0.4, and if the player gets

So we have

From there, we just plug the given values for

#P(H=h)=""_5C_h (0.4)^h(1-0.4)^(5-h)#

#P(H=3)=""_5C_3 (0.4)^3(0.6)^(5-3)#

#color(white)(P(H=3))=10 xx (0.4)^3(0.6)^2#

#color(white)(P(H=3))=10 xx 0.064 xx 0.36#

#color(white)(P(H=3))=0.2304#

So the probability of getting exactly 3 hits out of the next 5 at-bats is

#P(H=3)=0.2304" "=" "23.04%.#