Question

If a baseball player has a batting average of 0.265, what is the probability that the player will get the following number of hits in the next four times at bat?(A) Exactly 2 hits(B) At least 2 hits I have also attached a reference example.

Answer 1

For this case we have the following probability given:

p= 0.265

n= 4

Part a

`P(X=2)=(4C2)(0.265)^2(1-0.265)^(4-2)=0.2276`

Part b

`P(X\ge2)=P(X=2)+P(X=3)+P(X=4)`

Replacing we got:

`P(X=2)=(4C2)(0.265)^2(1-0.265)^2=0.2276`

`P(X=3)=(4C3)(0.265)^3(1-0.265)^1=0.0547`
`P(X=4)=(4C4)(0.265)^4(1-0.265)^0=0.0049316`

adding the two values we got:

`P(X>2)=0.2276+0.0547+0.0049316=0.287`