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Is this a conditional probability question P(B|A)=P(A), or is it asking for the probability of the Y

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Submitted : 2018-06-14 08:02:09    Popularity:     

Tags: question  probability  conditional  scoring  winning  

This season the probability that the Yankees will win a game is 1/3 and the probability that the Yankees will score 5 or more runs in a game is 3/8. The probability that the Yankees win or score more than 5 runs is 4/7. What is the probability that the Ya

Answers:

What events are A and B?

P(w) = 1/3
P(5+) = 3/8
P(w) U P(5+) = 4/7
1/3 + 3/8 = 17/24 which is not 4/7, so there is an intersection.
1/3 +3/8 -4/7 = 23/168 which is P(both)
(23/168)/(3/8) = 23/63

This is a conditional probability question.

A = Yankees will win
B = Yankees will score 5 or more runs

GivenL
P(A) = 1/3
P(B) = 3/8
P(A or B) = 4/7

P(A and B)
= P(A) + P(B) - P(A or B)
= (1/3) + (3/8) - (4/7)
= (56/168) + (63/168) - (96/168)
= 23/168

Probability that the Yankees will win when they score more than 5 runs
= P(A|B)
= P(A and B) / P(B)
= (23/168) / (3/8)
= (23/168) × (8/3)
= 23/63
= 0.4 (to the nearest tenth)

It's conditional probability. It's asking for the probability the Yankees win *when* (or *given*) they score more than 5 runs.

Let A be the event the Yankees win.
Let B be the event the Yankees score more than 5 runs.

You have:
P(A) = 1/3
P(B) = 3/8
P(A or B) = 4/7

Use this rule:
P(A or B) = P(A) + P(B) - P(A and B)

From that you can calculate:
P(A and B)

Then use this rule:
P(A|B) = P(A and B) / P(B)

I could calculate it out for you, but I've given you all the steps and I think you can take it from here.

It's conditional probability. What is the probability that they win, GIVEN that they score more than 5 runs.
That would be P(score more than 5 AND win) divided by P(score more than 5).

No



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