Some Probability question i can't figure out?

Question

Ques1 Two Evens, A and B. P(A) = 0.39, P(B) = 0.21, P(A or B) = 0.47. A and B are statistically dependent. Need to find P (Both A and B will occur)

What i think is we need to find  P(AB) which is = P(A/B) * P(B). Can't figure out how to find P(A/B)

Ques 2.

Assume that for two events A and B, P(A)=0.65 P(B)=.80, P(A/B) = P(A), P(B/A) = 0.85. Is this possible?

I think it is not since P(A/B) = P(A) it is case of independent marginal probability. Am i right?

? · Accepted Answer

Question 1:

P(A or B) - P(B) = 0.47 - 0.21 = 0.26 = P(A and not B)
P(A or B) - P(A) = 0.47 - 0.39 = 0.08 = P(B and not A)

P(A and B) = P(A or B) - P(A and not B) - P(B and not A)
= 0.47 - 0.26 - 0.08 = 0.13


Question 2:

If this situation were possible, then:
P(A and B) = P(B|A) P(A) = 0.85 * 0.65 = 0.5525
P(A and B) = P(A|B) P(B) = 0.65 * 0.80 = 0.52

So this situation would be possible only if 
0.5525 = 0.52
which, of course, it does not.

Some Probability question i can't figure out?

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