Question

5. Charlotte is picking out her class ring. She can select from a ruby, an emerald, or an opal stone, and she can also select silver or gold for the metal.

a. How many different combinations of one stone and one type of metal can she choose? Explain how you got your answer.
b. If Charlotte selects a stone and a metal at random, what is the probability that she would select a ring with a ruby stone and gold metal?

Answer 1

Explanation:

Given

Charlotte can select from a ruby , an emerald or an opal stone

i.e. there are 3 choices for stone

while there are 2 choices for metal i.e. silver or gold

no of ways to select a stone is
`^3C_1=3`

no of ways to select metal
`^2C_1=2`

No of ways to select a ring
`=2* 3=6`

(b)Probability of selecting a ruby is
`=(1)/(3)`

Probability of selecting a metal is
`=(1)/(2)`

Probability of selecting a ring with a ruby stone and gold metal
`=(1)/(3)* (1)/(2)=(1)/(6)`