Question

A box of chocolates contains five milk chocolates and five dark chocolates. You randomly pick a chocolate and eat it. Then you randomly pick another piece. What is the probability that both pieces are milk chocolate?

Answer 1

This is a probability question that has to do with the "without replacement" scenario, because every chocolate eaten leaves the box and never returns

The probability that both pieces are milk chocolate is calculated thus:

`\frac{Number\text{ of milk chocoltes}}{Total\text{ number of chocoltes in the box}}*\frac{Number\text{ of milk chocolates-1}}{Total\text{ number of chocoltes -1}}`

Number of milk chocolates = 5

NUmber of dark chocolates = 5

Total number of chocolates in the box = 5+5 =10

The probability that both pieces are milk chocolate is:

`\begin{gathered} (5)/(10)*(5-1)/(10-1)(since\text{ it is without replacement of chocolates)} \\ (5)/(10)*(4)/(9) \\ (20)/(90) \\ =(2)/(9) \end{gathered}`

The probability that both pieces are milk chocolate is:

`(2)/(9)`