What is the probability that the committee includes <strong>AT LEAST</strong> 2 ladies?
Consider the following for the two (02) items that follow :<br>A committee of 6 members is formed from a group of 7 gentlemen and 4 ladies.
- A. 41/66
- B. 47/66
- C. 49/66
- D. 53/66 ✓
Correct Answer: D. 53/66
Explanation
Probability of at least 2 ladies = 1 - P(\text{0 ladies}) - P(\text{1 lady}). P(\text{0 ladies}) = \frac{\binom{4}{0}\binom{7}{6}}{462} = \frac{7}{462}. P(\text{1 lady}) = \frac{\binom{4}{1}\binom{7}{5}}{462} = \frac{4 \times 21}{462} = \frac{84}{462}. So, required probability = 1 - \frac{91}{462} = \frac{371}{462} = \frac{53}{66}.
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