Question

An experiment succeeds twice as often as it fails, what is the probability that in the next five trials there will be 

(i) three successes and 

(ii) at least three successes.

Answer 1

Given a number of trials n = 5. 

Let P be the probability of success and q be the probability of failure. It is given that p = 2q.

(i) P (three successes) = P(X = 3)

= ⁵C₃(2/3)³ (1/3)²

= 10(8/27) (1/9) 

= 80/243

(ii) P( atleast three successes) = P(X ≥ 3) = 1 - P(X < 3)

= 1 - [P(X = 2) + P(X = 1) + P(X = 0)]

Thus the probability of at least three successes in five trials will be 192/423.