Question

The probability that a certain kind of component will survive a shock test is 3/4. Find the probability that exactly 2 of the next 4 components tested survive test, assuming tests are independent.

Answer 1

Therefore the required probability is
`=(27)/(128)`

Explanation:

The probability of success is
`(3)/(4)`

The number of trial = 4

X= the items survive out of 4

`P(x=r)=^nC_rq^(n-r)p^r` p =the probability of success and q = the probability failure.

p=
`(3)/(4)` and
`q=(1-(3)/(4))=(1)/(4)`

`\therefore P(X=2)=^4C_2((1)/(4) )^2((3)/(4) )^2`

`=(4!)/(2!2!) ((1)/(16) )((9)/(16) )`

`=(27)/(128)`

Therefore the required probability is
`=(27)/(128)`