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%.#