Question

Consider 5 independent Bernoulli.s trials each with probability of success p. If the probability of at least one failure is greater than or equal to 31 32 , then p lies in the interval : (1) ( 1 2 , 3 4 ] (2) ( 3 4 , 11 12 ] (3) [0, 1 2 ] (4) ( 11 12 ,1] A. ( 1 2 , 3 4 ] B. ( 3 4 , 11 12 ] C. [0, 1 2 ] D. ( 11 12 ,1] Select the correct answer from above options

Answer 1

Correct Answer - C Let X denote the number of failures in 5 trials. Then, P(X=r)=.5Cr(1-p)rp5-r,r=0,1,2,.....,5 . ∴P(X>1)≥ 31 32 ⇒1-P(X=0)≥ 31 32 ⇒1-p5≥ 31 32 ⇒ 1 32 ≥p5⇒p< 1 2 ⇒p∈[0,1/2]