SOLUTION: The probability that Ato , Sulley and Kofi will gain admission to a certain university are 4/5,3/4 and 2/3 respectively. Find the probability that : (a) none of them will gai

Algebra ->  Probability-and-statistics -> SOLUTION: The probability that Ato , Sulley and Kofi will gain admission to a certain university are 4/5,3/4 and 2/3 respectively. Find the probability that : (a) none of them will gai      Log On


   

Question 1114413: The probability that Ato , Sulley and Kofi will gain admission
to a certain university are 4/5,3/4 and 2/3 respectively.
Find the probability that :
(a) none of them will gain admission
(b) at most two of them will gain admission
(c) only Kofi and Ato will gain admission.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
The probability that Ato , Sulley and Kofi will gain admission
to a certain university are 4/5,3/4 and 2/3 respectively.
P(A) = 4/5, P(not A) = 1 - 4/5 = 1/5
P(S) = 3/4, P(not S) = 1 - 3/4 = 1/4
P(K) = 2/3, P(not K) = 1 - 2/3 = 1/3

Find the probability that :
(a) none of them will gain admission
P(not A)×P(not S)×P(not K) = (1/5)(1/4)(1/3) = 1/60

(b) at most two of them will gain admission
P(not all three) = 1 - P(all three) = 1 - P(A)×P(S)×P(K) =
1 - (4/5)(3/4)(2/3) = 1 - 2/5 = 3/5

(c) only Kofi and Ato will gain admission. 
P(K)×P(A)×P(not S) = (2/3)(4/5)(1/4) = 2/15

Edwin