The probability that certain type of component will survive a check test is 0.5. Find the probability that exactly tow of the next four componets will suvive.

Explanation

Let x= number of tested component survive
P = probability that the component suvieves the check test
`therefore p = 0.5 = 5/10 = 1/2 `
`therefore q =1 -p =1 -1/2 =1/2 `
Given : n =4
`therefore X ~ B(4,1/2)`
The p.m of X is given as :
` P [ X = x} =""^nC_xP^x q^(4-x)`
i.e `p(x) =""^4C_2(1/2)^x(1/2)^(4-x)=""^4C_x(1/2)^4`
`=""^4C_2(1/2)^4 = (4xx 3)/(1xx2)xx1/16 `
`= 3/8 = 0.375
Hence , the probability that exactly 2 of the 4 tested components suvive is 0.375.