Question

In baseball, a player pitches a ball from the mound to a catcher behind the plate. A pitch that passes over the plate above the batter’s knees and below his chest is a strike. All other pitches are “balls,” provided the batter does not swing at them or hit them foul.

The table below breaks a sample number of pitches into strikes and balls over the plate and not over the plate.

Which conditional probability below is either inaccurately described or inaccurately calculated?

a) The probability that a pitch not over the plate is a strike is zero. So, P(A | D) = 0.
b) The probability that a pitch not over the plate is a ball is 1. So, P(B | D) = 1.
c) The probability that a pitch over the plate is a strike is 10:15. So, ...
d) The probability that a pitch over the plate is a ball is 5:10. So, P(B | C) = 0.5.

Answer 1

The answer is A because I he probability that a pitch not over the plate is a strike

Answer 2

The correct option is d.

Explanation:

It the given table,

A : Plate is a strike.

B : Plate is a ball.

C : Pitch over the plate.

D : Pitch not over the plate.

Formula for conditional probability is

`P((A)/(B))=(P(A\cap B))/(P(B))`

a) The probability that a pitch not over the plate is a strike is zero. So,

`P((A)/(D))=(P(A\cap D))/(P(D))=(0)/(20)=0`

Therefore option 1 is accurately described or accurately calculated.

b) The probability that a pitch not over the plate is a ball is 1. So,

`P((B)/(D))=(P(B\cap D))/(P(D))=(20)/(20)=1`

Therefore option 2 is accurately described or accurately calculated.

c) The probability that a pitch over the plate is a strike is 10:15. So,

`P((A)/(C))=(P(A\cap C))/(P(C))=(10)/(15)=10:15`

Therefore option 3 is accurately described or accurately calculated.

d) The probability that a pitch over the plate is a ball is 5:10. So,

`P((B)/(C))=(P(B\cap C))/(P(C))=(5)/(15)=(1)/(3)=0.33`

Therefore option 4 is inaccurately calculated.

Hence the correct option is d.