Question

Barb has 25 sweets.

She has 17 liquorice sweets, 3 mint sweets and 5 humbugs.
Barb is going to take at random two sweets.
Work out the probability that the two sweets will not be the same type of sweet.
Give your answer as a fraction.

Answer 1

The total number of ways to pick 2 sweets from 25 is 25C2 = 300.

The ways to pick 2 sweets type same the of are:

- 2 liquorice sweets: 17C2 = 136

-2 mint sweets: 3C2 = 3

- 2 humbugs: 5C2 = 10

So, the total number of ways to pick 2 sweets of the same type is 136 + 149 =10 +3.

Therefore, the number of ways to pick 2 sweets of different types is 300 - 149 = 151.

So, the probability that the two sweets will not be the same type of sweet is 151/300.

Explanation: