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A bag contains 15 caps. 8 black caps and 7 red caps. If two caps are drawn at random, what is the probability that at least one is red cap?

A bag contains 15 caps. 8 black caps and 7 red caps. If two caps are drawn at random, what is the probability that at least one is red cap? Correct Answer 11/15

Given:

Number of black caps: 8

Number of red caps: 7

Formula used:

P(E) = Number of favorable outcomes/total number of outcomes

Calculation:

When one is red cap and one is black cap drawn: 7C1 × 8C1

⇒ ×

⇒ 7 × 8

⇒ 56

When both the caps are red drawn: 7C2

⇒ 7 × 6 × 5!/2 ! × 5!

⇒ 21

Total number of outcomes: 15C2

⇒ 15 × 14 × 13!/2 ! × 13!

⇒ 105

P(E) = (56 + 21)/105

⇒ 77/105

⇒ 11/15

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