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

Answer:

The exact probability = 0.0431

Step-by-step 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 = $\frac{12}{36}=\frac{1}{3}$

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 =  $\frac{11}{35}$

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

Total items in the bag=34

Probability of picking a bar of dark chocolate =  $\frac{14}{34}=\frac{7}{17}$

The exact probability of picking the items:

$=\frac{1}{3}\times\frac{11}{35}\times\frac{7}{17}$

$=\frac{77}{1785}$

$=0.0431$

Therefore, the exact probability = 0.0431

Answer 2

10+12+14 = 36

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

There's your answer.