Question 847499
p (the probability of not arriving on time)= 2/5 from our first statement.

We can also figure out that n = 8.

a)  binomial with n=8, x= 3, p =2/5

(8 choose 3)(2/5)^3 *(3/5)^5 = .2787

b) binomial with n=8 x=2 (since arriving on time is considered a failure, 8-6 = 2 successes), and p = 2/5

(8 choose 2) * (2/5)^2 * (3/5)^6 = .2090

If you'd like, change your definition of success to be on time.  Then n=8, p =3/5 x = 6

(8 choose 6) * (3/5)^6 * (2/5)^2 = .2090

Partitioning 8 into 6 and 2 is the same as partitioning 8 into 2 and 6. This is why we get the same result. Just remember to know what you consider a success and the rest will fall into place.