the probabilities that 3 friends A,B andC pass a driving test are1/3,1/4,2/5 respectively.All 3 take the test find the probability that(a)aa 3 failed the test (b) only B passes the test(c) only 2 of them pass the test (d)at least 1 passes the test...

I will do one. Assuming the events are independent...

Prob (all fail)=Prob(Afails)*prob(bfails)*prob(cfails)
= 2/3 * 3/4 * 3/5

To find the probability that all three friends failed the test, you need to multiply the probabilities of each friend failing individually.

Let's denote the events as follows:
P(A) = probability that friend A passes the test = 1/3
P(B) = probability that friend B passes the test = 1/4
P(C) = probability that friend C passes the test = 2/5

(a) To find the probability that all three friends failed the test, you can calculate:
P(A') * P(B') * P(C'), where ' denotes the complement of an event.
So, the probability that all three friends failed the test is:

P(A') = 1 - P(A) = 1 - 1/3 = 2/3
P(B') = 1 - P(B) = 1 - 1/4 = 3/4
P(C') = 1 - P(C) = 1 - 2/5 = 3/5

Therefore, the probability that all three friends failed the test is:
P(all fail) = P(A') * P(B') * P(C') = (2/3) * (3/4) * (3/5) = 18/60 = 3/10.

By following the same logic, you can calculate the probabilities for the remaining parts (b), (c), and (d).