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.




Over plate (Event C)


Not over plate (Event D)


Strike (Event A) 10 0

Ball (Event B) 5 20


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

The probability that a pitch not over the plate is a ball is 1. So, P(B | D) = 1.

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

The probability that a pitch over the plate is a ball is 5:10. So, P(B | C) = 0.5.

The probability that a pitch not over the plate is a strike is zero. So, P(A | D) = 0.
I have no clue how to do this. Show your work.

Answer 1

To solve this question, you just need to count all the probability of the options.

The probability that a pitch not over the plate is a strike is zero. So, P(A | D) = 0.

True. It is 0/0+20= 0

The probability that a pitch not over the plate is a ball is 1. So, P(B | D) = 1.

True, it is 20/20+0= 1

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

Incomplete but it sounds to be true. It should be 10/10+5= 10/15 = 2/3

The probability that a pitch over the plate is a ball is 5:10. So, P(B | C) = 0.5.

Answer 2

Answer:

The probability that a pitch over the plate is a ball is 5:10. So, P(B | C) = 0.5.

Step-by-step explanation:

P(B | C) = n(B & C)/n(C)

= 5/(10+5)

= 5/15

5 : 15