14.Probability
medium

$A$ और $B$ ऐसी घटनाएँ दी गई हैं जहाँ $P(A)=\frac{1}{2}, P(A \cup B)=\frac{3}{5}$ तथा $P ( B )=p$
$\bar{p}$ का मान ज्ञात कीजिए यदि घटनाएँ परस्पर अपवर्जी हैं।

A

$\frac {1}{10}$

B

$\frac {1}{10}$

C

$\frac {1}{10}$

D

$\frac {1}{10}$

Solution

It is given that $P(A)=\frac{1}{2},\, P(A \cup B)=\frac{3}{5}$ and $P(B)=p$

When $A$ and $B$ are mutually exclusive, $A \cap B=\phi$

$\therefore P(A \cap B)=0$

It is known that, $P(A \cup B)=P(A)+P(B)-P(A \cap B)$

$\Rightarrow \frac{3}{5}=\frac{1}{2}+p-0$

$\Rightarrow p=\frac{3}{5}-\frac{1}{2}=\frac{1}{10}$

Standard 11
Mathematics

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.