I have a bag of caramels hidden in the drawer of my desk. The bag contains 30 light caramels, 15 dark caramels, and 55 rather tasteless wooden cubes.
Suppose I draw two caramels, replacing the first before drawing the second. What is the probablility that I will draw a light caramel on the first trial and a light one on the second?
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The question is a little ambiguous as it is not clear whether ,in the first instance, the 'tasteless wooden cubes' should be discarded as the question refers to actually drawing caramels without considering the possibility of drawing a cube instead. Therefore, they are not part of the ratio as there is no possibility (from the wording of the question) of them being drawn. If there was, the process would be the same but the ratio would be out of 100 and not 45 and you would change your fractions accordingly.
There are 45 caramels altogether of which the ratio of light to dark is 30:15
This can be written as a fraction because there are '30 out of 45'
and 15 out of 45. We can simplify the fractions:
`30/45= 2/3` light caramels and
`15/45=1/3` dark caramels
There is a 2 out of 3 chance that a light caramel will be drawn the first time and the second time becauses the first caramel is replaced before the second one is taken.
Note that had the first caramel not been replaced the ratio would have changed to 30 out of 44 and then simplified.
The answer can be written in various ways:
P(a) = 2:3 or 2/3 or 66,6 (recurring)%
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