First slide

Theorems of probability

Question

P(A $\cap$ B) = $\frac{1}{4}$ , $P (\bar{A}) = \frac{1}{3}, P (B) = \frac{1}{2}$ , then $P (\bar{A} \cap \bar{B}) =$

Easy

A

$\frac{1}{12}$
B

$\frac{11}{12}$
C

$\frac{1}{4}$
D

$\frac{3}{4}$

Solution

$P (A \cap B) = \frac{1}{4}, P (A) = \frac{2}{3}, P (B) = \frac{1}{2}$
$P (\bar{A} \cap \bar{B}) = 1 - P (A \cup B)$

$= 1 - (\frac{2}{3} + \frac{1}{2} - \frac{1}{4})$ $= \frac{1}{12}$

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