NDA 2026 · PYQ · Probability / Geometric Mean · medium
Let A, B, C and D be mutually exclusive and exhaustive events and P(A)/2 = P(B)/3 = P(C)/5 = P(D)/8. If G is the geometric mean of P(A), P(B), P(C) and P(D), then what is 9G equal to?
A.17^(1/4)✓ Correct
B.15^(1/4)
C.13^(1/4)
D.11^(1/4)
Explanation
With k = 1/18: P(A) = 2/18, P(B) = 3/18, P(C) = 5/18, P(D) = 8/18. G = [(2·3·5·8)/18⁴]^(1/4) = [240/18⁴]^(1/4) = 240^(1/4)/18. So 9G = 9·240^(1/4)/18 = 240^(1/4)/2 = (240/16)^(1/4) = 15^(1/4). Answer is (b) 15^(1/4).
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