The probability that a person who undergoes a kidney operation will be recovered is 0.5 .Find the probability that of the 6 patients who undergo similar operations
(a) noen will recover. (March 16.)
(b) half of them will recover . (oct 13, March ' 16 july 19)

Explanation

Let X = number of patients who reconvered from operation.
p = probability that a person recovered from kidney operation
`therefore p = 0.5 = 5/ 10 = 1/2 `
`therefore q = 1- p = 1 - 1/2 =1/2 `
Given : n =6
`therefore X ~ B (6, 1/ =2)`
The . p.m of X is given as
P [X=x] `= ""^nC_xP^xq^(n-x)`
i.e ,. `p(x) = ""^6C_0(1/2)^x(1/2)^(6-x)=""^6C_x(1/2)^6, " " x= 0,1,2,...,6`
(a) P (none will recover ) `=P [X =0] =p(0)`
`=""^6C_3(1/2)^6=1xx 1/64 =1 /64 = 0.015625 `
Hence , the probability that none of the patients will recover is 0.3125 .