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 \\ (n)/(N)=(8)/(28)=(2)/(7) \\ 2nd_{\text{ }}case\colon \\ (n-1)/(N-1)=(7)/(27) \end{gathered}`

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

`(2)/(7)\cdot(7)/(27)=0.074`

Answer:

7.4%