If A and B are two independent events such that P,(A cap B') = frac{3}{{25}} and P,(A' cap B

English

Gujarati

Hindi

14.Probability

medium

If $A$ and $B$ are two independent events such that $P\,(A \cap B') = \frac{3}{{25}}$ and $P\,(A' \cap B) = \frac{8}{{25}},$ then $P(A) = $

A

$\frac{1}{5}$

B

$\frac{3}{8}$

C

$\frac{2}{5}$

D

$\frac{4}{5}$

(IIT-2002)

Solution

(a) Since events are independent.

So, $P(A \cap B') = P(A) \times P(B') = \frac{3}{{25}}$

$ \Rightarrow P(A) \times \{ 1 – 2P(B)\} = \frac{3}{{25}}$ …..$(i)$

Similarly, $P(B) \times \{ 1 – P(A)\} = \frac{8}{{25}}$ …..$(ii)$

On solving $(i)$ and $(ii)$, we get $P(A) = \frac{1}{5}$ and $\frac{3}{5}$.

Standard 11

Mathematics

Share

Similar Questions

A box contains $10$ good articles and $6$ with defects. One article is chosen at random. What is the probability that it is either good or has a defect

easy

A fair coin with $1$ marked on one face and $6$ on the other and a fair die are both tossed. find the probability that the sum of numbers that turn up is $12$.

easy

The chance of getting a doublet with $2$ dice is

easy

A box contains $6$ nails and $10$ nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, what is the probability that it is rusted or is a nail

easy

In a game, a man wins $Rs.\,100$ if he gets $5$ or $6$ on a throw of a fair die and loses $Rs.\,50$ for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is

hard

(JEE MAIN-2019)