Question

An experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least 3 successes.

Answer 1

Probability of getting success(p) =`3/4`

Probability of getting failure(q)`=1/4`

No. of trials=5

`P(X>=3)=P(X=3)+P(X=4)+P(X=5)`

`P(X=r)=""^nC_rq^(n-r)p^r`

`P(X>=3)=""5C_3(1/4)^(5-3)(3/4)^3+""5C_4(1/4)^(5-4)(3/4)^4+""5C_5(1/4)^(5-5)(3/4)^5`

`P(x>=3)=(10xx27)/1024+(5xx81)/1024+243/1024`

`P(X>=3)=918/1024=459/512`