MHT CET · Maths · Probability
A family has 3 children. The probability that all the three children are girls, given that at least one of them is a girl is
- A \(\frac{7}{8}\)
- B \(\frac{1}{8}\)
- C \(\frac{1}{7}\)
- D \(\frac{2}{7}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{7}\)
Step-by-step Solution
Detailed explanation
\(P(\text{all girls} \cap \text{at least one girl}) = P(\text{GGG}) = \frac{1}{8}\) \(P(\text{at least one girl}) = 1 - P(\text{all boys}) = 1 - P(\text{BBB}) = 1 - \frac{1}{8} = \frac{7}{8}\)
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