Question

Sara has 20 sweets.

12 liquorice, 5 mint, 3 humbug.
Sara is going to take at random two sweets.
work out the probability that the two sweets will not be the same type. Give your answer as a fraction.

Answer 1

The probability that the two sweet will not be same type is
`(111)/(190)`

Explanation:

P(two sweets not same) = 1 - P( two sweets will be same)

There are 3 possible outcomes where two sweets will be same.

1. it can be two liquor-ice, 2. it can be 2 mint and 3. it can be two humbug

P(two liquor-ice)
`=(12)/(20) *(11)/(19)= (33)/(95)`

P(two mint)
`=(5)/(20) * (4)/(19) =(1)/(19)`

P(tow humbug)
`=(3)/(20) *(2)/(19) =(3)/(190)`

Now we have:

P(two sweets not same) = 1 - P( two sweets will be same)

`=1- \left((33)/(95)+ (1)/(19)+ (3)/(190) \right)`

`1-(79)/(190)`

`=(111)/(190)`

Therefore, the probability that the two sweet will not be same type is
`(111)/(190)`