Financial Risk Manager Part 1
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During a disease outbreak, the probability of surviving after an infection is 60%. Determine the probability that at least 8 out of a group of 9 infected persons will survive.
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Community
NNikitesh
A
0.7
B
0.07
C
0.007
D
0.06
Explanation:
This is a binomial probability problem where:
- n = 9 (number of trials)
- p = 0.6 (probability of success/survival)
- q = 1 - p = 0.4 (probability of failure/death)
We need P(X ≥ 8) = P(X = 8) + P(X = 9)
Using the binomial formula: P(X = x) = C(n,x) * p^x * q^(n-x)
P(X = 8) = C(9,8) * (0.6)^8 * (0.4)^1 = 9 * 0.01679616 * 0.4 = 9 * 0.006718464 = 0.060466176
P(X = 9) = C(9,9) * (0.6)^9 * (0.4)^0 = 1 * 0.010077696 * 1 = 0.010077696
P(X ≥ 8) = 0.060466176 + 0.010077696 = 0.070543872 ≈ 0.0705 or 7%
Therefore, the correct answer is 0.07 (Option B).
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