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:

111/190

Step-by-step explanation:i know you dont want to see explanation so yeah...

Answer 2

Probabilities are used to determine the chances of an event.

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

The given parameters are:

$n = 20$ --- number of sweet

$L = 12$

$M = 5$

$H = 3$

First, we calculate the probability that the two selected sweet will be of the same type.

This is calculated as:

$P(Same) =P(L\ and\ L) + P(M\ and\ M) + P(H\ and\ H)$

Because the selection is without replacement, the equation becomes

$P(Same) = \frac{12 \times 11}{20 \times 19} +\frac{5 \times 4}{20 \times 19} + \frac{3 \times 2}{20 \times 19}$

$P(Same) = \frac{132}{380} +\frac{20}{380} + \frac{6}{380}$

Add fractions

$P(Same) = \frac{132+20+6}{380}$

$P(Same) = \frac{158}{380}$

Using the complement rule, the probability that the two selected sweet will not be of the same type is:

$P(Not\ same) = 1 - P(Same)$

This gives

$P(Not\ same) = 1 - \frac{158}{380}$

Take LCM

$P(Not\ same) = \frac{380 - 158}{380}$

$P(Not\ same) = \frac{222}{380}$

Simplify

$P(Not\ same) = \frac{111}{190}$

Hence, the required probability is: $\frac{111}{190}$

Read more about probabilities at:

https://brainly.com/question/11234923