Question

Marilyn has 10 caramels, 12 mints, and 14 bars of dark chocolate in a bag. She picks three items from the bag without replacement.

The exact probability that Marilyn picks a mint, then another mint, and finally a bar of dark chocolate is -------?

Answer 1

10+12+14 = 36

12/36 x 11/35 x 14/34 = 11/255

There's your answer.

Answer 2

The exact probability = 0.0431

Explanation:

Given: A bag contain - Caramels= 12, mints= 12, bars of dark chocolates= 14

Marilyn picks three items from the bag without replacement.

Total number of items 12+12+14=36

Now, probability = favorable outcome / total no. of outcomes

Probability of picking a mint =
`(12)/(36)=(1)/(3)`

After picking a mint there are :

caramels=10, mints=11, bars of chocolate=14

Total items in the bag=35

Probability of picking another mint =
`(11)/(35)`

now, caramels=10, mints=10, bars of chocolate=14

Total items in the bag=34

Probability of picking a bar of dark chocolate =
`(14)/(34)=(7)/(17)`

The exact probability of picking the items:

`=(1)/(3)*(11)/(35)*(7)/(17)`

`=(77)/(1785)`

`=0.0431`

Therefore, the exact probability = 0.0431