In testing a certain kind of truck tire over rugged terrain, it is found that 25% of the trucks fail to complete the test run without a blowout. of the next 15 trucks tested, find the probability that (a) from 3 to 6 have blowouts; (b) fewer than 4 have blowouts; (c) more than 5 have blowouts.

The given question is a binomial distribution

Probability for binomial distribution = P = nCr * (p)^r  *  (q)^(n-r)

where p = probability of success(.25)

q = probability of failure(.75)

n = total outcomes

r = required number of outcomes

1- P(from 3 to 6 have blowouts) = P(3<=X<=6)= P(X= 3)+P(X= 4)+P(X= 5)P(X= 6)

2- P(fewer than 4 have blowouts) = P(X=0) +  P(X=1)  + P(X=2) + P(X=3)

3- P(more than 5 have blowouts)= 1- P(X<= 5) = 1-[ P(X=0) +  P(X=1)  + P(X=2) + P(X=3) + P(X=4) + P(X=5) ]

correct answer:

i^31 = -i