Thread: Probability of Rain occuring

If the probability of rain is 60% on each of three consecutive days, find:
1)the probability that it rains on all three days,
2)the probability that it rains on exactly two of the three days?
For number 1 my anwer was .064 and for number 2 my answer was .288, am I correct? If not can you help me please?

Originally Posted by journeygirl280

If the probability of rain is 60% on each of three consecutive days, find:
1)the probability that it rains on all three days,
2)the probability that it rains on exactly two of the three days?
For number 1 my anwer was .064 and for number 2 my answer was .288, am I correct? If not can you help me please?

It would help if you told us why you think these are the answers.

The number of days out of 3 that is rains in a binomial random variable with
distribution B(3, 0.6), for which:

p(n; 3, 0.6) = 3!/(n!(3-n)!) 0.6^n (1-0.6)^{3-n}.

For (1), n=3, and so:

p(3; 3, 0.6) = 0.6^3 ~= 0.216.

For (2), n=2, and so:

p(2; 3, 0.6) = 3 (0.6^2) (0.4) ~= 0.432

RonL

Thank you for your help which leads me to another question. What is the relationship between the answers and the binomial expansion of
(0.4 + 0.6)^3. I know that the binomial expansion equals 1 but how does that relate to the answers you got?