type the correct answer in the box. if necessary, use / for the fraction bar. marilyn has 10 caramels, 12…

type the correct answer in the box. if necessary, use / for the fraction bar. 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

type the correct answer in the box. if necessary, use / for the fraction bar. 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

Explanation:

Step1: Calculate total items

The total number of items in the bag is $10 + 12+14=36$.

Step2: Calculate probability of first - pick

The probability of picking a mint first is $\frac{12}{36}$.

Step3: Calculate probability of second - pick

Since there is no replacement, after picking a mint first, there are $36 - 1=35$ items left and $12-1 = 11$ mints left. So the probability of picking a mint second is $\frac{11}{35}$.

Step4: Calculate probability of third - pick

After picking two mints, there are $35 - 1=34$ items left and 14 bars of dark - chocolate. So the probability of picking a bar of dark - chocolate third is $\frac{14}{34}$.

Step5: Calculate combined probability

The probability of the three - step event is the product of the probabilities of each step. So $P=\frac{12}{36}\times\frac{11}{35}\times\frac{14}{34}=\frac{12\times11\times14}{36\times35\times34}=\frac{1848}{42840}=\frac{11}{255}$.

Answer:

$\frac{11}{255}$