# The probability that a patient recovers from a stomach disease is 0.8. Suppose 20 people are known to have contracted this disease. What is the probability that exactly 14 recover?

Question
Binomial probability
The probability that a patient recovers from a stomach disease is 0.8. Suppose 20 people are known to have contracted this disease. What is the probability that exactly 14 recover?

2021-02-20
Let Y be the random variable denoting the number of patients that recover from the stomach disease. Y is clearly a binomial random variable as each patient will either recover or not recover (i.e. has only 2 values).
Here, n = 20 and p = 0.8
We need to find P(Y = 14). This can be found by using Table I in Appendix 3 with n =20 and p = 0.8
$$P(Y = 14) = P(Y \leq 14) - P(Y \leq 13)$$
$$= 0.196 - 0.087$$
$$= 0.109$$
Result: $$P(Y = 14) = 0.109$$

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P.vaiue Pevgiue
P-value f P-value
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