Question 847499: assume that 2 out 5 shipments coming from a particular supplier do not arrive on time. what is the probability that among 8 shipments which this supplier send, a.)exactly 3 will not arrive on time b.) exactly 6 will arrive on time
Answer by swincher4391(1107)   (Show Source):
You can put this solution on YOUR website! 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.
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