IIT-JEE 2008 · Paper 2 · Mathematics Q6

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MathematicsSingle correct+3 / -1Question 6 of 66

An experiment has 10 equally likely outcomes. Let $A$ and $B$ be two non-empty events of the experiment. If $A$ consists of 4 outcomes, the number of outcomes that $B$ must have so that $A$ and $B$ are independent, is

2, 4 or 8

3, 6 or 9

4 or 8

5 or 10

Answer and worked solution

Official answer: D

Independence. $P(A\cap B)=P(A)P(B)$ with $P(A)=\frac4{10}$ and $P(B)=\frac b{10}$ :
$\frac{|A\cap B|}{10}=\frac{4b}{100}\implies|A\cap B|=\frac{2b}5.$
This must be a whole number, so $b$ is a multiple of 5: $b=5$ (with $|A\cap B|=2$ ) or $b=10$ .

(D)

Topics:Independent events

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IIT-JEE 2008 · Paper 2, Mathematics question 6