Question

A bag of 30 tulip bulbs contains 12 red tulip bulbs, 13 yellow tulip bulbs, and 5 purple tulip bulbs. You want to buy 2 bulbs and select them at random, find a) P(both are red) b) P(first is yellow and second is red) c) P(none are purple)

Answer 1

A bag of 30 tulip bulbs contains 12 red tulip bulbs, 13 yellow tulip bulbs, and 5 purple tulip bulbs.

We want to buy 2 bulbs and select them at random.

$a) P(both\: are\: red) = \frac{\binom{12}{2}}{\binom{30}{2}}=\frac{66}{435}$

$b) P(first\: is\: yellow\: and\: second\: is\: red) = \frac{\binom{13}{1}\times \binom{12}{1} }{\binom{30}{2}}=\frac{156}{435}$

$c) P(none\: are\: purple) = \frac{\binom{25}{2} }{\binom{30}{2}}=\frac{300}{435}$

(none are purple is equivalent to saying that both are among remaining red and yellow so 12+13 = 25)