Question

A package of chocolates contains 3 caramel-filled pieces, 3 raspberry-filled pieces and 4 fudge-filled pieces. What is the probability that someone will reach in and select a caramel-filled piece, keep it, and then select a raspberry-filled piece?

Answer 1

We r taking the p(A) as the probability of the caramel filled and p(B) as the probability of raspberry filled. Check out the picture it has the workings in it. Hope it helps

Answer 2

The probability that someone will reach in and select a caramel-filled piece, keep it, and then select a raspberry-filled piece from the package is $\frac{1}{3}$.

Given,

A package of chocolates contains 3 caramel-filled pieces, 3 raspberry-filled pieces and 4 fudge-filled pieces.

To Find,

The probability that someone will reach in and select a caramel-filled piece, keep it, and then select a raspberry-filled piece.

Solution,

The method of finding the probability that someone will reach in and select a caramel-filled piece from the package, keep it, and then select a raspberry-filled piece is as follows -

We know that the probability of an event is equal to $\frac{number \ of \ ways \ that \ the\ event \ can\ occur }{number \ of \ total\ possible\ events}$.

There is a total of 10 chocolates of different types.

So the probability that someone will get a caramel-filled piece of chocolate is $\frac{3}{10}$.

After keeping the caramel-filled piece of chocolate, there will be $(10-1)=9$ chocolates in the package.

Then the probability that someone will pick up a raspberry-filled piece is $\frac{3}{9} =\frac{1}{3}$.

So the probability of happening the two events simultaneously is $\frac{3}{10}*\frac{1}{3}=\frac{1}{10}$.

Hence, the probability that someone will reach in and select a caramel-filled piece, keep it, and then select a raspberry-filled piece from the package is $\frac{1}{10}$.

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