Applied Mathematics

Algebra

Medium

A die is thrown. If A is the event 'the number appearing is a multiple of 3 and B is the event 'the number appearing is even', then A and B are

dependent events

independent event

$P(A \cap B) = \frac{1}{3}$

$P(B) = \frac{1}{3}$

✅ Correct Option: 2

A = multiples of 3 = {3, 6}, so $P(A) = \frac{2}{6} = \frac{1}{3}$ .

B = even numbers = {2, 4, 6}, so $P(B) = \frac{3}{6} = \frac{1}{2}$ .

$A \cap B = \{6\}$ , so $P(A \cap B) = \frac{1}{6}$ .

Since $P(A) \cdot P(B) = \frac{1}{3} \cdot \frac{1}{2} = \frac{1}{6} = P(A \cap B)$ , the events are independent.

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Solution