Question

A box has 15 candies in it: 4 are taffy, 3 are butterscotch, and 8 are peppermint Josh wants to select two candies to eat for dessert. The first candy will be selected at random, and then the second candy will be selected at random from the remaining candies. What is the probability that the two candies selected are butterscotch? Do not round your intermediate computations. Round your final answer to three decimal places

Answer 1

Total number of candies = 15

number of buterscotch = 3

number of taffy = 4

number of peppermint = 8

The probability that the first candy will be butterscotch =  

Number of possible outcomes Total number of outcomes

=   $\frac{3}{15}$

Here the outcome is getting butterscotch candy.

After taking the first butterscotch candy the number of butterscotch candies will reduce to 2

and the total number of candies will become 14

So after taking the first candy,

Total number of candies = 14

Number of butterscotch = 2

Therefore the probability that the second candy is also a butterscotch will be=  

Number of possible outcomes Total number of outcomes

= $\frac{2}{14}$

The probalities that the two candies are butterscotch is the product of their probabilities =  $\frac{3}{15}\,\times \,\frac{2}{14}$

=0.0286