JEE Advanced · 2008 · 13 Apr 2008 · Paper 2 · Probability XII

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

(A)2, 4 or 8
(B)3, 6 or 9
(C)4 or 8
(D)5 or 10✓ Correct

Answer: (D)

Solution

For independence,

P (A \cap B) = P (A) \cdot P (B)

. Let

B

have

p

outcomes. Then

P (A) = \frac{4}{10} = \frac{2}{5}

and

P (B) = \frac{p}{10}

. The number of outcomes in

A \cap B

must be

\frac{4 p}{10} = \frac{2 p}{5}

, which must be an integer. This requires

2 p

to be divisible by 5, so

p

must be a multiple of 5. Since

1 \leq p \leq 10

, we have

p = 5

p = 10

JEE Advanced · 2008 · 13 Apr 2008 · Paper 2 · Single correct option

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