Answer to Question #211053 in Electrical Engineering for Muhammad Yousaf

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)


1
Expert's answer
2021-06-28T08:54:02-0400

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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