The probability that a person who undergoes kidney operation will recover is 0.5. Find the probability that of six patients who undergo similar operations. (a) Non will recover. (b) Half of them will recover.

Explanation

Since there are six patients, `n=6.` If a patient recovers, the outcome is a success.
Thus, `P=p` (success) `=0.5and q=1-p=0.5`
Let X: No. of patents, who recovered out of 6. Then `X~B(n=6,p=0.5)`
The p.m.f. of X is given as,
`P(X=x)=p(x) ""^(6)C_(x)(0*5)^(x)(0*3)^(6-x), x=0, 1,2,3,4,5,6.`
(i) Probability (non will reconver) `=P (X=0)`
`=""^(6)C_(0)(0*5)^(0)(0.5)^(6)`
`=(1)*(1)*(0*5)^(6)`
`=0*015625`
(ii) Probability (half of them will recover)=P `(X=3)`
`=""^(6)C_(3)(0*5)^(3)(0*5)^(3)`
`=20xx0*125xx0*125=0*3125`