# Statistics question: What is P(A'|B)?

I am doing stats and my question is... What is P(A'|B)?

Given: P(A) = 0.30, P(B') = 0.50, P(B) = 0.50, P(A') = 0.70, P(A intersect B') = 0.10, P(A intersect B) = 0.70....

I would really appreciate the help.... thanks!

CORRECTION: P(A in union with B) = 0.70 not P(A intersect B) = 0.70

### 2 Answers

- ≈ nohglfLv 79 years agoFavorite Answer
P(A' | B) = P(A' and B) / P(B)

P(A|B) = P(A and B) / P(B)

You can verify using a Venn diagram that

P(A' and B) + P(A and B) = P(B)

and so

P(A'| B) + P(A|B) = 1

So Let's find P(A|B).

Step 1: Find P(A intersect B)

P(A U B) = P(A) + P(B) - P(A intersect B)

0.70 = 0.30 + 0.50 - P(A intersect B)

So

P(A intersect B) = 0.10

Step 2: Find P(A|B)

P(A|B) = P(A intersect B) / P(B)

= 0.10 / 0.50

= 0.20

So P(A|B) = 0.20.

Step 3: Find P(A' | B)

Since

P(A' | B) + P(A | B) = 1

Then

P(A' | B) = 1 - P(A | B)

= 1 - 0.20

= 0.80

So P(A' | B) = 0.80.

Solution: P(A' | B) = 0.80.

Source(s): ____________ P(A' | B) = P(A' and B) / P(B) P(A | B) = P(A and B) / P(B) P(A' | B) + P(A | B) = [P(A' and B) + P(A and B)] / P(B) Since P(A' and B) + P(A and B) = P(B), then P(A' | B) + P(A | B) = P(B) / P(B) = 1- Login to reply the answers

- Anonymous9 years ago
P(A'| B) + P(A|B) = 1

Now, P(A|B)=P(A intersect B) / P(B)

Need to find P(A intersect B).

P(A intersect B) =P(B)+P(A)-P(A union B) [As, P(A union B)=P(B)+P(A)-P(A intersect B)]

=0.50+0.30-0.70

=0.10

So, P(A|B)=0.10/0.50

=0.20

Therefore, P(A'| B) = 1- P(A|B)

=1-0.20

=0.80 (Ans.)

Source(s): http://tutorteddy.com- Login to reply the answers