In a study of 20 individuals participating in an experimenta

In a study of 20 individuals participating in an experimental medical procedure the probability of each individual surviving the procedure is .82. If the procedure is performed on all 20 participants at the same time compute the probability that at least one does not survive the procedure.

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
p=1-0.82=0.18(because 0.82 is the probability of surviving, we need its inverese, so subtract with 1.)

P( X < 1) = P(X=0)   
= ( 20 0 ) * 0.18^0 * ( 1- 0.18 ) ^20 +
= 0.0189

P( X > = 1 ) = 1 - P( X < 1) = 0.9811