Balls and cubes in an urn

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Question from Dave, a student:

In an urn, there are 80 objects of two kinds: cubes (C) and balls (B). An object can be either red (R) or green (G).
Note that all the four combinations are possible and that the number of cubes is not necessarily equal to the number of
balls. Similarly, the number of red objects is not necessarily equal to the number of green objects. Someone tells us that
in the urn there are 20 red cubes, 50 balls, and 30 red objects. An object is randomly selected from the urn.
(a). What is the probability that a green ball is selected?
(b). If we know that a cube has been selected, what is the probability that it's red?
(c). If we know that a red object has been selected, what is the probability that it's a cube?

Hi Dave,

I constructed a table to describe the setup. The body of the table is 2 by 2 with the two rows representing the colours, red and green and the columns representing the shapes, cubes or balls. In the margins are row and column sums and in the lower right corner is total number of objects which is 80. I filled in the numbers you know.

	cubes	balls
red	20		30
green
		50	80

Since there are 30 red objects and 20 of them are cubes the remainder, 30 - 20 = 10 must be balls.

	cubes	balls
red	20	10	30
green
		50	80

In a similar way you can fill in the remainder of the table.

Once the table is complete you can use it to calculate the probabilities. Let us know if you have difficulty completing the problem.

Harley

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.