Question

A snack-size bag of M&Ms candies is opened. Inside, there are 12 red candies, 12 blue, 7 green, 13 brown, 3 orange, and 10 yellow. Three candies are pulled from the bag in succession, without replacement. What is the probability that the first two candies drawn are orange and the third is green?

Answer 1

`(1)/(4180)`

Explanation:

GIVEN: A snack-size bag of M&Ms candies is opened. Inside, there are
`12` red candies,
`12` blue,
`7` green,
`13` brown,
`3` orange, and
`10` yellow. Three candies are pulled from the bag in succession, without replacement.

TO FIND: What is the probability that the first two candies drawn are orange and the third is green.

SOLUTION:

Total candies in the bag
`=57`

Probability that first ball is orange,
`P(A)=\frac{\text{total orange candies in bag}}{\text{total candies in bag}}`

`=(3)/(57)=(1)/(19)`

Probability that second ball is orange,
`P(B)=\frac{\text{total orange candies in bag}}{\text{total candies in bag}}`

`=(2)/(56)=(1)/(28)`

Probability that third ball is green,
`P(C)=\frac{\text{total green candies in bag}}{\text{total candies in bag}}`

`=(7)/(55)`

Now, probability that first two balls are orange and third is green is

`=P(A)* P(B)* P(C)`

`=(1)/(19)*(1)/(28)*(7)/(55)`

`=(1)/(19)*(1)/(4)*(1)/(55)`

`=(1)/(4180)`

Hence, probability that first two balls are orange and third is green is
`(1)/(4180)`