Question bank/JEE Main/Mathematics

A and B are two independent events. The probability that both A
and B occur simultaneously is $\frac{1}{6}$ and the probability that
neither of them occur is $\frac{1}{3}$. Then the probability of
occurrence of event A is.
A vkSj B nks Lora= ?kVuk,sa gS rFkk A rFkk B ds,d lkFk gksus $\frac{1}{6}$ gS rFkk mu
izkf;drk $\frac{1}{3}$ gS rc ?kVuk A

A+ PB- P(A cap B) = frac Rightarrow P

Show answer and solution▾

[IMAGE] $\Rightarrow$ $1 - P(A \cup B) = \frac{1}{3} \Rightarrow$
$P(A \cup B) = \frac{2}{3}$
$\Rightarrow$
$P(1) + P(2) - P(A \cap B) = \frac{2}{3} \Rightarrow P(1) + P(2) - \frac{1}{6} = \frac{2}{3}$
$\Rightarrow$ $P(1) + P(2) = \frac{5}{6}$.......(1)
Also blfy, $P(A \cap B) = P(1) \cdot P(2) = \frac{1}{6}$..........(ii)
Solving (i) & (ii) P(1) $= \frac{1}{2}$  or  $\frac{1}{3}$

Source: Grass-G / M-21 Mathematics Paper 19 Dec Hindi Eng.docx