Answer to Question #188911 in Statistics and Probability for Kel

Question

3.) You have a box filled with 10 light bulbs. Seven are good, three are not. You pick light bulbs at random. You do not put them back after you pick them out (without replacement). You pick two out of the box. What is the chance that:

a.) Neither is good? 

b.) Both are good?

c.) Only one is good? 

Answer 1

We have a collection of 10 light bulbs.

Good bulbs = 7

Defective bulbs = 3

You pick two out of the box

No. of ways of selecting two bulbs $= ^{10}C_2$

a.) Chance that neither is good $= \dfrac{^3C_2 \times ^7C_0}{^{10}C_2}$

b.) Chance that both are good = $\dfrac{^7C_2 \times ^3C_0}{^{10}C_2}$

c.) Chance that only one is good $= \dfrac{^7C_1 \times ^3C_1}{^{10}C_2}$