Question

There is a bag with only milk and dark chocolates.

The probability of randomly choosing a dark chocolate is
7
9
.
There are 42 dark chocolates in the bag and each is equally likely to be chosen.
Work out how many milk chocolates there must be.

Answer 1

12 milk chocolates.

Explanation:

-We know that probabilities add upto 1:

`P(milk)+P(dark)=1\\\\P(milk)+(7)/(9)=1\\\\P(milk)=(2)/(9)`

Let X be the total number of chocolates. We know that probability is the successful events divided by the total number of events:

`P(dark)=(dark \ events)/(total \ events)\\\\\\(7)/(9)=(42)/(X)\\\\X=54`

#We subtract the number of dark chocolates from X to get the number of milk chocolates:

`N_m=X-N_d\\\\=54-42\\\\=12`

Hence, there must be 12 milk chocolates.