Question

A and b are events such that p(a u b)=3/4 p(a n b)=1/4 p(a bar)=2/3 then p(abar n b)is

Answer 1

$\textbf{Given:}$

$\text{P(A \cup B)= \frac{3}{4} , P( \overline{A} )= \frac{2}{3} and P(A \cap B)= \frac{1}{4} }$

$\text{Now}$

$\text{P( \overline{A} )=1-P(A)}$

$\text{P(A)=1-P( \overline{A} )}$

$\text{P(A)=1- \frac{2}{3} }$

$\textbf{P(A)= \bf\frac{1}{3} }$

$\text{We know that}$

$\text{P( \overline{A}\cap B)=P(A \cup B)-P(A)}$

$\text{P( \overline{A}\cap B)=}\frac{3}{4}-\frac{2}{3}$

$\text{P( \overline{A}\cap B)=}\frac{9-8}{12}$

$\implies\textbf{P( \bf\overline{A}\cap B)=}\bf\frac{1}{12}$

Find more:

Let A and B be two events such that P(A)=0.6, P(B) = 0.2 and P(A/B)=0.5. Then P (A'/B')

equals

(a) 1/10

(b) 3/10

(C) 3/8

(d) 6/7​

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