32. a package of chocolates contains 3 caramel - filled pieces, 3 raspberry - filled pieces and 4 fudge…

32. 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?\na. $\frac{1}{30}$\nb. $\frac{1}{15}$\nc. $\frac{1}{10}$\nd. $\frac{3}{50}$

32. 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?\na. $\frac{1}{30}$\nb. $\frac{1}{15}$\nc. $\frac{1}{10}$\nd. $\frac{3}{50}$

Answer

Explanation:

Step1: Calculate total number of chocolates

The total number of chocolates is $3 + 3+4=10$.

Step2: Calculate probability of first - pick

The probability of selecting a caramel - filled piece first is $\frac{3}{10}$ since there are 3 caramel - filled pieces out of 10 total pieces.

Step3: Calculate probability of second - pick

After keeping the caramel - filled piece, there are 9 chocolates left. The probability of selecting a raspberry - filled piece second is $\frac{3}{9}=\frac{1}{3}$.

Step4: Calculate combined probability

Since these are independent events, we multiply the probabilities. So the combined probability is $\frac{3}{10}\times\frac{1}{3}=\frac{3}{30}=\frac{1}{10}$.

Answer:

C. $\frac{1}{10}$