An urn contains 5 red and 2 black balls. Two balls are drawn at random with replacement. Let X be the number of black balls drawn. What is the variance of X?
Answer and explanation
Correct answer: C. 20 / 49
- Step 1: Probability of drawing black ball p = 2 / (5 + 2) = 2/7.
- Step 2: q = 1 - p = 5/7. Number of trials n = 2.
- Step 3: For binomial distribution B(n, p): Var(X) = n p q = 2 (2/7) (5/7) = 20 / 49.
Why not the others: The alternative choices (10 / 49, 25 / 49, 4 / 49) stem from algebraic sign mistakes, misapplying coordinate formulas, or intermediate arithmetic calculation slips.
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