P(A cup B) = P(A cap B) if and only if relation between P(A) and P(B) is

English

Gujarati

Hindi

14.Probability

normal

$P(A \cup B) = P(A \cap B)$ if and only if the relation between $P(A)$ and $P(B)$ is

A

$P(A) = P(\bar A)$

B

$P\,(A \cap B) = P(A' \cap B')$

C

$P\,(A) = P\,(B)$

D

None of these

(IIT-1985)

Solution

(c) $P(A) = P(B)$

As this gives $P(A \cup B) = P(A) + P(B) – P(A \cap B)$

or $P(A) = 2P(A) – P(A)$$ \Rightarrow P(A \cup B) = P(A \cap B).$

Standard 11

Mathematics

Share

Similar Questions

The probability that a man will be alive in $20$ years is $\frac{3}{5}$ and the probability that his wife will be alive in $20$ years is $\frac{2}{3}$. Then the probability that at least one will be alive in $20$ years, is

medium

Prove that if $E$ and $F$ are independent events, then so are the events $\mathrm{E}$ and $\mathrm{F}^{\prime}$.

medium

Given two independent events $A$ and $B$ such $P(A)=0.3,\,P(B)=0.6 .$ Find $P($ neither $A$or $B)$

easy

Suppose that $A, B, C$ are events such that $P\,(A) = P\,(B) = P\,(C) = \frac{1}{4},\,P\,(AB) = P\,(CB) = 0,\,P\,(AC) = \frac{1}{8},$ then $P\,(A + B) = $

easy

The probability that a leap year selected at random contains either $53$ Sundays or $53 $ Mondays, is

medium