A die is thrown 6 times. If getting an odd number is considered a success, what is the probability of getting at least 5 successes?
Answer and explanation
Correct answer: A. 7 / 64
- Step 1: p = 3/6 = 1/2, q = 1/2, n = 6.
- Step 2: P(X ≥ 5) = P(X = 5) + P(X = 6).
- Step 3: P(X = 5) = C(6, 5) (1/2)^6 = 6 (1/64) = 6/64.
- Step 4: P(X = 6) = C(6, 6) (1/2)^6 = 1 (1/64) = 1/64.
- Step 5: P(X ≥ 5) = 6/64 + 1/64 = 7/64.
Why not the others: The alternative choices (5 / 64, 3 / 32, 1 / 8) stem from algebraic sign mistakes, misapplying coordinate formulas, or intermediate arithmetic calculation slips.
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