Answer :
Answer:
111 / 190
Step-by-step explanation:
Let us first compute the probability of picking 2 of each sweet. Take liquorice as the first example. There are 12 / 20 liquorice now, but after picking 1 there will be 11 / 19 left. Thus the probability of getting two liquorice is demonstrated below;
[tex]12 / 20 * 11 / 19 = \frac{33}{95},\\Probability of Drawing 2 Liquorice = \frac{33}{95}[/tex]
Apply this same concept to each of the other sweets;
[tex]5 / 20 * 4 / 19 = \frac{1}{19},\\Probability of Drawing 2 Mint Sweets = 1 / 19\\\\3 / 20 * 2 / 19 = \frac{3}{190},\\Probability of Drawing 2 Humbugs = 3 / 190[/tex]
Now add these probabilities together to work out the probability of drawing 2 of the same sweets, and subtract this from 1 to get the probability of not drawing 2 of the same sweets;
[tex]33 / 95 + 1 / 19 + 3 / 190 = \frac{79}{190},\\1 - \frac{79}{190} = \frac{111}{190}\\\\[/tex]
The probability that the two sweets will not be the same type of sweet =
111 / 190
