[tex]\frac{111}{190}[/tex] is the probability that the two biscuits were of not the same type.
What is Probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.
According to question, Carolyn has 20 biscuits in a tin.
She has 12 plain biscuits, 5 chocolate biscuits and 3 ginger biscuits
Carolyn takes at random two biscuits from the tin.
We have to find out the probability that the two biscuits were of not the same type.
P(plain biscuit, plain biscuit) [tex]=(\frac{12}{20} )(\frac{11}{19} )=\frac{132}{380}[/tex]
P(chocolate biscuit, chocolate biscuit)[tex]=(\frac{5}{20})(\frac{4}{19} )=\frac{20}{380}[/tex]
P(ginger biscuit, ginger biscuit)[tex]=(\frac{3}{20}) (\frac{2}{19})=\frac{6}{380}[/tex]
Probability of same type of biscuits
[tex]=\frac{132}{380} +\frac{20}{380}+\frac{6}{380}[/tex]
[tex]=\frac{79}{190}[/tex]
The probability that the two biscuits were not of the same type.
[tex]=1-\frac{79}{190}[/tex]
[tex]=\frac{111}{190}[/tex]
Hence, we can conclude that [tex]\frac{111}{190}[/tex] is the probability that the two biscuits were not of the same type.
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