A trial succeeds with probability 1/3. It is repeated 3 times independently. What is the probability of exactly 2 successes?
Answer and explanation
Correct answer: C. 2/9
- Step 1: The number of successes is binomial with n = 3 and p = 1/3.
- Step 2: P(X = 2) = C(3,2) p^2 (1-p)^1 = 2/9.
Answer
2/9.
Why not the others: The binomial coefficient and both powers are needed; the other values leave out the coefficient, use the wrong exponent or give the complementary probability.
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