# Thread: Basic Probability Problem

1. ## Basic Probability Problem

A box contains four 40-W bulbs, five 60-W bulbs, and six 75-W bulbs. If bulbs are selected one by one in random order (without replacement), what is the probability that at least two bulbs must be selected to obtain one that is rated 75 W?
Im not really sure where to go with this problem, if someone could lead me in the right direction or offer a solution it would be greatly appreciated! Thanks!

2. Hello, BiGpO6790!

It's a bit tricky . . . I wouldn't call it "basic".

A box contains: four 40w bulbs, five 60w bulbs, six 75w bulbs.
If bulbs are selected one by one in random order (without replacement),
what is the probability that at least two bulbs must be drawn to obtain a 75w bulb?

If a problem asks for "at least" or "at most",
. . it is often easier to consider the opposite probability.

The opposite of "two or more drawn to get a 75w bulb"
. . is: "less than two drawn to get a 75w bulb."

$\displaystyle P(\text{0 drawn and get a 75w}) \:=\:0$

$\displaystyle P(\text{1 drawn and get a 75w}) \:=\:\frac{6}{15} \:=\:\frac{2}{5}$

Hence: .$\displaystyle {P(\text{less than 2 drawn and get 75w}) \:=\:0 + \frac{2}{5} \:=\:\frac{2}{5}$

Therefore: .$\displaystyle P(\text{at least 2 drawn and get 75w}) \;=\;1 - \frac{2}{5} \;=\;\boxed{\frac{3}{5}}$

Someone check my reasoning and my math . . . please!