If P(A)=0.8,P(B)=0.9,and P(A∩B)=0.8, what is P(B∣A)? What about P(A∣B)?

P(B∣A)=1 P(A∣B)=89=0.888 Explanation: If P(A)=P(A∣B) then A⊆B so given B it follows that A is certain. One way to look at it is to suppose there were 1000 events P(A)=0.8 tells us that 800 of those events were of type A P(A∩B)=0.8 tells us that 800 of the 1000 are both A and B So all the A events are "used up" in (A∩B) Using the 1000 event example: P(B)=0.9 tells us 900 of the 1000 events are of type B 800 of the 900 type B events are of type A, so P(A∣B)=800900=89

Best solutions to - "If P(A)=0.8,P(B)=0.9,and P(A∩B)=0.8, what is P(B∣A)? What about"

High School
Statistics and Probability
High school probability
Probability

Racetovb4j

Answered question

2022-02-14

P (A) = 0.8, P (B) = 0.9, and P (A \cap B) = 0.8

, what is

P (B ∣ A)

? What about

P (A ∣ B)

Answer & Explanation

ashuhra6e

Beginner2022-02-15Added 15 answers

P (B ∣ A) = 1

P (A ∣ B) = \frac{8}{9} = 0.888

Explanation:
If

P (A) = P (A ∣ B) then A \subseteq B

so given B it follows that A is certain.
One way to look at it is to suppose there were 1000 events

P (A) = 0.8

tells us that 800 of those events were of type A

P (A \cap B) = 0.8

tells us that 800 of the 1000 are both A and B
So all the A events are "used up" in

(A \cap B)

Using the 1000 event example:

P (B) = 0.9

tells us 900 of the 1000 events are of type B 800 of the 900 type B events are of type A, so

P (A ∣ B) = \frac{800}{900} = \frac{8}{9}

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