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

caramels=10
mints=12
bars=14
total items in the bag=10+12+14=36
probability of picking a mint = 12/36=1/3
After picking a mint there are
caramels=10
mints=11
bars=14
total items in the bag=35
probability of picking another mint = 11/35
now,
carmels=10
mints=10
bars=14
total items=34
probability of picking a bar =14/34
the exact probability of picking the items in the given sequence is the joint probability
that is (12/36)*(11/35)*(14/34)=0.02240543161

Answer 2

Marilyn has 10 caramels, 12 mints, and 14 bars of dark chocolate in a bag
Total = 10 + 12 + 14 = 36

1st pick a mint: 12/36 = 1/3
2nd pick a mint: 11/35
3rd pick dark chocolate: 14/34 = 7/17

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

1/3 x 11/35 x 7/17 = 77 / 1785 = 11/255

Answer
11/255