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Question
A critical orthopedic surgery is performed on 3 patients. The probability of recovering
a patient is 0.6. Then the probability that after surgery, exactly two of them will recover
is
🎥 Video solution / Text Solution of this question is given below:
Given:
- Number of patients = 3
- Probability of recovery p=0.6
- Probability of failure q=1−p=0.4
We want: Probability that exactly 2 recover out of 3.
? Use Binomial Probability Formula:
P(X = r) = \binom{n}{r} p^r (1 - p)^{n - r} where n = 3, r = 2, p = 0.6
? Calculation:
P(X = 2) = \binom{3}{2} (0.6)^2 (0.4)^1 = 3 \times 0.36 \times 0.4 = 0.432
✅ Final Answer: \boxed{0.432}
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