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
