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

Answer:

The probability that the two sweet will not be same type is $\frac{111}{190}$

Step-by-step 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) $=\frac{12}{20} \times\frac{11}{19}= \frac{33}{95}$

P(two mint) $=\frac{5}{20} \times \frac{4}{19} =\frac{1}{19}$

P(tow humbug) $=\frac{3}{20} \times\frac{2}{19} =\frac{3}{190}$

Now we have:

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

                                  $=1- \left(\frac{33}{95}+ \frac{1}{19}+ \frac{3}{190} \right)$

                                   $1-\frac{79}{190}$

                                   $=\frac{111}{190}$

Therefore, the probability that the two sweet will not be same type is $\frac{111}{190}$