Question

Solve the problem that involves probabilities with events that are not mutually exclusive.There are 28 chocolates in a box, all identically shaped. There are 6 filled with nuts, 14 with caramel, and 8 are solid chocolate. Yourandomly select one piece, eat it, and then select a second piece. Find the probability of selecting 2 solid chocolates in a row.

Answer 1

Let:

n = Number of solid chocolates = 8

N = Total number of chocolates = 28

$\begin{gathered} 1st_{\text{ }}case\colon \\ \frac{n}{N}=\frac{8}{28}=\frac{2}{7} \\ 2nd_{\text{ }}case\colon \\ \frac{n-1}{N-1}=\frac{7}{27} \end{gathered}$

So, the probability of selecting 2 solid chocolates in a row are:

$\frac{2}{7}\cdot\frac{7}{27}=0.074$

Answer:

7.4%