First slide

Theorems of probability

Question

$Let A and B are any two events such that P (A) = \frac{1}{2} and$ $P (B) = \frac{1}{3} then the value of P {(A^{c} \cap B^{c})}^{c} + P {(A^{c} \cup B^{c})}^{c} has the value =$

Moderate

A

$\frac{2}{3}$
B

$\frac{3}{4}$
C

$\frac{4}{5}$
D

$\frac{5}{6}$

Solution

$\begin{aligned} P (A) = \frac{1}{2}; P (B) = \frac{1}{3} \\ P {(A^{c} \cap B^{c})}^{c} = P (A \cup B) \\ P {(A^{c} \cup B^{c})}^{c} = P (A \cap B) \end{aligned}$
On adding, we get
$∴ L.H.S. = P (A) + P (B) = \frac{5}{6}$

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