Exercise: If probability of recovery for severe PEM with infection is 0.4 and 5 children arewith severe PEM and infection, find out the probability that five will recover, four willrecover and four or more will recover?
Question
Exercise: If probability of recovery for severe PEM with infection is 0.4 and 5 children arewith severe PEM and infection, find out the probability that five will recover, four willrecover and four or more will recover?
Solution
This problem can be solved using the binomial probability formula, which is:
P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))
where:
- P(X=k) is the probability of k successes in n trials
- C(n, k) is the combination of n items taken k at a time
- p is the probability of success
- n is the number of trials
- Probability that all five will recover:
Here, n=5 (number of children), k=5 (all five recover), and p=0.4 (probability of recovery).
P(X=5) = C(5, 5) * (0.4^5) * ((1-0.4)^(5-5)) = 1 * (0.01024) * (1) = 0.01024
- Probability that four will recover:
Here, n=5, k=4, and p=0.4.
P(X=4) = C(5, 4) * (0.4^4) * ((1-0.4)^(5-4)) = 5 * (0.0256) * (0.6) = 0.0768
- Probability that four or more will recover:
This is the sum of the probabilities that exactly four and exactly five will recover.
P(X>=4) = P(X=4) + P(X=5) = 0.0768 + 0.01024 = 0.08704
So, the probability that all five will recover is 0.01024, the probability that exactly four will recover is 0.0768, and the probability that at least four will recover is 0.08704.
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