Suppose an auditor has 18 tax returns 12 of which are for ph

Suppose an auditor has 18 tax returns, 12 of which are for physicians. If three of the 18 tax returns are randomly selected, then what is the probability that at least one of the three selected will be a physicians tax return?

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( X < 1) = P(X=0)   
= ( 3 0 ) * 0.6667^0 * ( 1- 0.6667 ) ^3
= 0.037

P( X > = 1 ) = 1 - P( X < 1) = 0.963