AP EAMCET · Maths · Probability
A four member committee is to be formed from a group containing 9 men and 5 women. If a committee is formed randomly, then the probability that it contains atleast one woman is
- A \(\frac{125}{143}\)
- B \(\frac{18}{143}\)
- C \(\frac{60}{143}\)
- D \(\frac{65}{143}\)
Answer & Solution
Correct Answer
(A) \(\frac{125}{143}\)
Step-by-step Solution
Detailed explanation
Total ways to form a committee: \( \binom{14}{4} = \frac{14 \times 13 \times 12 \times 11}{4 \times 3 \times 2 \times 1} = 1001 \) Ways to form a committee with all men: \( \binom{9}{4} = \frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1} = 126 \) Probability of…
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