Answer to Question #267237 in Statistics and Probability for mora

Question

A technician is launching fireworks near the end of a show. Of the remaining ten fireworks, five are blue and five are red. If he launches five of them in a random order, what is the probability that all of them are blue? (Give answer as a percent)

Answer 1

You want 5 of the 5 she chooses to be blue, which means 0 are red. There are 5 blue and 5 red remaining.

She is choosing 5 of the remaining 10 fireworks; the number of ways she can do that is "10 choose 5".

You want the probability that of those 5, 5 are blue and 0 are red. So she needs to choose 5 of the 5 remaining blue fireworks (5 choose 5) and 0 of the remaining 5 red fireworks (5 choose 0).

$= \frac{C(5,5)\times C(5,0)}{C(10,5)}$

$=\frac{1\times1}{252}$

$=\frac{1}{252}\times 100\%$

$=0.3968\%$