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 strike is zero. So, P(A | D) = 0. 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.

Answer 1

Option: D is inaccurately calculated.

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

Explanation:

We will calculate each of the options and then observe which of the option is incorrectly calculated.

We are given a table as:

over the plate (C) Not over the plate(D) Total

strike(A) 10 0 10

Ball(B) 5 20 25

Total 15 20 35

We know that:

`P(A|B)=(P(A\bigcap B))/(P(B))`

Now:

1)

`P(A|D)=(P(A\bigcap D))/(P(D))`

From the table we have:

`P(A\bigcap D)=0`

Hence, P(A|D)=0.

Hence, option 1 is correct.

2)

Now:

`P(B|D)=(P(B\bigcap D))/(P(D))`

from the table we have:

P(B∩D)=20=P(D)

Hence, P(B|D)=0.

Hence, option 2 is correct.

3)

Now:

`P(A|C)=(P(A\bigcap C))/(P(C))`

from the table we have:

P(A∩C)=10 and P(C)=15

Hence, P(A|C)= 10/15.

Hence, option 3 is correct.

4)

`P(B|C)=(P(B\bigcap C))/(P(C))`

from the table we have:

P(B∩C)=5 and P(C)=15.

Hence, P(B|C)=5/15=1/3.

Hence, option 4 is incorrectly calculated.

Hence, the answer is:

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

Answer 2

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.
False. It should be 5/10+5= 5/15 = 1/3