Given three indentical bags each containing 10 balls, whose colou… - Vidyadip

MCQ

Given three indentical bags each containing 10 balls, whose colours are as follows :

	Red	Blue	Green
Bag I	3	2	5
Bag II	4	3	3
Bag III	5	1	4

A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is p and if the balls is Green, the probability that it is from bag III is $q$, then the value of $\left(\frac{1}{p}+\frac{1}{q}\right)$ is :

A
6
B
9
C
7
D
8

✓

Answer

$\mathrm{p}=\mathrm{P}\left(\frac{\mathrm{B}_{\mathrm{I}}}{\mathrm{R}}\right)=\frac{\frac{1}{3}\left(\frac{3}{10}\right)}{\frac{1}{3}\left(\frac{3}{10}+\frac{4}{10}+\frac{5}{10}\right)}=\frac{1}{4}$
$\mathrm{q}=\left(\frac{\mathrm{B}_{\text {III }}}{\mathrm{G}}\right)=\frac{\frac{1}{3}\left(\frac{4}{10}\right)}{\frac{1}{3}\left(\frac{5}{10}+\frac{3}{10}+\frac{4}{10}\right)}=\frac{1}{3}$
$\therefore \frac{1}{\mathrm{p}}+\frac{1}{\mathrm{q}}=7$

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