Question

Calculate the probability that 3 or fewer rainy days occur during the next 15 days. The probability any day is rainy is .2.

For this question I tried using binomial distribution by setting x = 0, 1, 2, 3. p=.2 and n =15. After doing all of them, Do add the probabilities to get the answer?

Answer 1

To get the probability that <I>all</I> events would occur, you need to <I>multiply</I> the probability of each of the individual events.

The probablitiy of no rainy days is .8^15.

The probability of one rainy day is .2 * .8^14.

The probability of two rainy days is .2^2 * .8^13.

The probability of three rainy days is .2^3 * .8^12.

The probability of being either one or the other of these four probabilities is found by adding the four products above.

I hope this helps. Thanks for asking.