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AP EAMCET · Maths · Probability

In a school there are 3 sections A, B and C. Section A contains 20 girls and 30 boys, section B contains 40 girls and 20 boys and section C contains 10 girls and 30 boys. The probabilities of selecting the section \(\mathrm{A}, \mathrm{B}\) and C are \(0.2,0.3\) and 0.5 respectivley. If a student selected at random from the school is a girl, then the probability that she belongs to section A is

  1. A \(\frac{121}{200}\)
  2. B \(\frac{16}{121}\)
  3. C \(\frac{14}{81}\)
  4. D \(\frac{16}{81}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{16}{81}\)

Step-by-step Solution

Detailed explanation

\( P(G|A) = \frac{20}{50} = 0.4 \) \( P(G|B) = \frac{40}{60} = \frac{2}{3} \) \( P(G|C) = \frac{10}{40} = 0.25 \) \( P(G) = P(G|A)P(A) + P(G|B)P(B) + P(G|C)P(C) \) \( P(G) = (0.4)(0.2) + (\frac{2}{3})(0.3) + (0.25)(0.5) = 0.08 + 0.2 + 0.125 = 0.405 \)…