Question

A box of chocolates contains 5 milk chocolates, 4 dark chocolates, and 3 white chocolates. What is the probability that you randomly select a milk chocolate first, replace it, and then select a white chocolate? *

Answer 1

10.42% probability that you randomly select a milk chocolate first, replace it, and then select a white chocolate

Explanation:

Since the chocolate is replaced, the first selection and the second are independent of each other.

Independent events:

If two events, A and B, are independent.

`P(A \cap B) = P(A)P(B)`

In this question:

Event A: Selecting a milk chocolate first.

Event B: Selecting a white chocolate.

5+4+3 = 12 chocolates. Of those, 5 are milk.

This means that
`P(A) = (5)/(12)`

3 are white.

This means that
`P(B) = (3)/(12) = (1)/(4)`

What is the probability that you randomly select a milk chocolate first, replace it, and then select a white chocolate?

`P(A \cap B) = P(A)P(B) = (5)/(12)*(1)/(4) = (5)/(48) = 0.1042`

10.42% probability that you randomly select a milk chocolate first, replace it, and then select a white chocolate