Question

A cricket umpire has to pick 6 caps and 4 sweaters before a match. She picks up 3 articles at random. Determine the probability that at least one sweater was picked by the umpire ?

• A. 1/6
• B. 1/12
• C. 2/3
• D. 5/6
• E. 5/11

Hint:

``At least one'' problems are easier via complement: P(at least 1) $= 1 -$ P(none). Here P(0 sweaters) $= \binom{6}{3}/\binom{10}{3} = 20/120 = 1/6$.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Use complementary counting: P(at least 1 sweater) = 1 $-$ P(no sweater).

Step 2: Detailed Explanation:
Total articles = $6+4=10$. Total ways to pick 3 = $\binom{10}{3} = 120$. P(no sweater) = all 3 from 6 caps $= \binom{6}{3} = 20$. P(no sweater) $= \dfrac{20}{120} = \dfrac{1}{6}$. P(at least 1 sweater) $= 1 - \dfrac{1}{6} = \dfrac{5}{6}$.

Step 3: Final Answer:
The probability is $\dfrac{5}{6}$.