5 6 We voss has a carton of twelve eggs Unbeknownst to her T

We v_oss has a carton of twelve eggs. Unbeknownst to her. Two of them have gone bad. She makes breakfast for herself and her husband using, four of the eggs. What is the probability that... ...all of the eggs she uses are still good{i.e. no bad eggs]? ...both bad eggs end up in the breakfast? it is estimated that the balance, what is the probability that... ...it is between $1100 and $1440? ...it is at least $750? ...it is less than $16000?

Solution

a)
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 = 0 ) = ( 4 0 ) * ( 0.1667^0) * ( 1 - 0.1667 )^4
= 0.4822
b)
P( X = 2 ) = ( 4 2 ) * ( 0.1667^2) * ( 1 - 0.1667 )^2
= 0.1158