A biased coin is tossed 5 times. The probability of obtaining heads on any single toss is p = 0.6. What is the probability of getting exactly 3 heads?
Answer and explanation
Correct answer: C. 0.3456
- Step 1: Apply the Binomial Probability Formula: P(X = k) = C(n, k) p^k (1 - p)^(n - k).
- Step 2: Here n = 5, k = 3, p = 0.6, and 1 - p = 0.4.
- Step 3: Compute C(5, 3) = 10.
- Step 4: Compute p^3 = (0.6)^3 = 0.216.
- Step 5: Compute (1 - p)^2 = (0.4)^2 = 0.16.
- Step 6: Multiply: 10 0.216 0.16 = 10 * 0.03456 = 0.3456.
Answer
0.3456.
Why not the others: '0.2304' is the probability of getting exactly 4 heads; '0.1536' is the probability of getting 3 tails; '0.4000' is an unweighted estimation.
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