# Thread: probability ? june 2006 math b regents

1. ## probability ? june 2006 math b regents

hi, so i need some serious step by step explanation for this problem. i've got the math b regents tomorrow and im freaking out because i don't know how to do this probability stuff still lol

here's a copy of the problem:

Ginger and Mary Anne are planning a vacation trip to the island of Capri, where the probability of rain on any day is 0.3. What is the probability that during their five days on the island, they have no rain on exactly three of the five days?

any help would be greatly appreciated. thanks in advance!

clare.

2. Originally Posted by supahfly
hi, so i need some serious step by step explanation for this problem. i've got the math b regents tomorrow and im freaking out because i don't know how to do this probability stuff still lol

here's a copy of the problem:

Ginger and Mary Anne are planning a vacation trip to the island of Capri, where the probability of rain on any day is 0.3. What is the probability that during their five days on the island, they have no rain on exactly three of the five days?

any help would be greatly appreciated. thanks in advance!

clare.
The probability of no rain for a given three days is obviously $\displaystyle (0.7)^3 (0.3)^2$.

But you can choose 3 days from 5 days in $\displaystyle {5 \choose 3}$ ways.

So the required probability is $\displaystyle {5 \choose 3} (0.7)^3 (0.3)^2$.

(This is an example of the binomial distribution).