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AP EAMCET · Maths · Probability

There are three families \(F_1, F_2, F_3. F_1\) has 2 boys and 1 girl; \(F_2\) has 1 boy and 2 girls; \(F_3\) has 1 boy and 1 girl. A family is randomly chosen and a child is chosen from that family randomly. If it is known that the child thus selected is a girl, then the probability that she is from \(\mathrm{F}_2\) is

  1. A \(\frac{4}{9}\)
  2. B \(\frac{2}{9}\)
  3. C \(\frac{3}{7}\)
  4. D \(\frac{5}{7}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{4}{9}\)

Step-by-step Solution

Detailed explanation

\(P(F_1)=P(F_2)=P(F_3)=\frac{1}{3}\) \(P(G|F_1)=\frac{1}{3}, P(G|F_2)=\frac{2}{3}, P(G|F_3)=\frac{1}{2}\) \(P(G) = P(G|F_1)P(F_1) + P(G|F_2)P(F_2) + P(G|F_3)P(F_3)\)…