Question #211053

If two events, A and B, are such that P(A) = .5, P(B) = .3, and P(AnB) = 1, find

the following

a. P(A|B)

b. P(B|A)

c. P(A|A UB)

d. P(A|ANB)

e. P(ANB|AUB)

Expert's answer

a. P(A|B)

"\\frac{P(AnB)}{P(B)}=\\frac{0.2}{0.5}=\\frac{2}{5}"

b. P(B|A)

"\\frac{P(BnA)}{P(A)}=\\frac{0.2}{0.3}=\\frac{2}{3}"

c. P(A|A UB)

"\\frac{P(An(AnB))}{P(AuB)}=\\frac{P(A)}{P(AuB)}=\\frac{0.5}{0.5+0.3-0.1}=\\frac{0.5}{0.7}=\\frac{5}{7}"

d. P(A|ANB)

"\\frac{P((A)n(P(AnB))}{P(AuB)}=\\frac{P(A)}{1-P(AnB)}=\\frac{0.5}{1-0.1}=\\frac{0.5}{0.9}=\\frac{5}{9}"

e. P(AnB|AUB)

"\\frac{P((AnB)(AuB))}{P(AuB)}=\\frac{P(AnB)}{P(AuB)}=\\frac{0.2}{0.5+0.3-0.1}=\\frac{0.2}{0.7}=\\frac{2}{7}"

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