[Jessicafin94]

Sunti has two boxes of crayons, A and B.
In box A he has a red, blue, yellow and black crayon.
In box B he has a red, yellow and blue crayon.
Sunti takes a crayon at random from each box.

a) Draw a sample space diagram to show all the possible outcomes.
b) Work out the probability that the crayon will be
I) both red ii) the same colour iii) different colours

[ebaines]

I won't solve your problem for you, but I will give an example of a slightly different problem. Suppose Box A has red, blue, and green pencils, and box B has just red and blue pencils. You draw a sample space diagram by first showing three possible choices for Box A, and then for each of those there showing the two additional choices for box B. You also write the probability of each leg above it. To find the probability of any path you multiply the probabilities of each leg that make up that path. For example the probability of getting two red pencils is 1/3 x 1/2 = 1/6. If you add up the probabilities for all possible paths it should equal 1 (this is a good check to make sure you haven't made a mistake). For this example the probability of getting two of the same color is the sum of the probability of getting 2 reds plus the probability of getting 2 blue, which is (1/3 x 1/2) + (1/3 x 1/2) = 1/3. The probability of getting different colors is the sum of the probability of the four different paths that represent red-blue, blue-red, greed-red, and green-blue (as an aside, it's also equal to one minus the probability of getting matching pencils). Hope this helps. Tell us what you get for answers to part (b).