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A box has 14 candies in it: 3 are taffy, 7 are butterscotch, and 4 are caramel. Juan wants to select two candies to eat for dessert. The first candy will be selectedat 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 taffy?Do not round your intermediate computations. Round your final answer to three decimal places.



Answer :

Okay, here we have this:

Considering the provided information we are going to calculate what is the probability that the two candies selected are taffy. So, for this, first we are going to calculate the probability that the first is taffy, and then the probability that the second is taffy. Finally we will multiply these two probabilities to find the total probability.

Remember that the simple probability of an event is equal to favorable events, over possible events.

First is taffy:

At the beginning there are 14 sweets, and 3 are taffy, so there are 3 favorable events and 14 possible, then:

First is taffy=3/14

Second is taffy:

Now, in the bag there are 13 sweets left, and of those 2 are taffy, so now there are 2 favorable events out of 13 possible:

Second is taffy=2/13

The first and second are taffy:

First is taffy*Second is taffy=3/14*2/13

First is taffy*Second is taffy=3/91

First is taffy*Second is taffy=0.033

First is taffy*Second is taffy=3.3%

Finally we obtain that the probability that the two candies selected are taffy is aproximately 0.033 or 3.3%.

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