Multiple choice

An urn $A$ contains $2$ white and $3$ black balls. Another urn $B$ contains $3$ white and $4$ black balls.Out of these two urns, one is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that I. It is from urn $A$ is $21/40$, II. It is from urn $B$ is $20/41$ Which of the following statements is correct

  1. I only

  2. II only

  3. both I and II

  4. neither I nor II
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Urn A: 2W, 3B (Total 5). Urn B: 3W, 4B (Total 7). P(A) = 1/2, P(B) = 1/2. P(B|A) = 3/5, P(B|B) = 4/7. P(Black) = (1/2 * 3/5) + (1/2 * 4/7) = 3/10 + 4/14 = 21/70 + 20/70 = 41/70. P(A|Black) = (3/10) / (41/70) = 21/41. P(B|Black) = (20/70) / (41/70) = 20/41. Statement II is correct.

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