In a proobabolity experiment, three containers have the following contents.

A jar contains 2 white dice and 3 black dice.

A white box contains 5 red ballls and 3 green balls

A black box contains 4 red balls and 3 green balls

One die is taken at random form the jar. If the die is white, two balls are taken form the white box, at random and without repalcement. If the die is black, two balls are taken from the black box, at random and without replacement. Events W and M are defined as follows

W: A white die is taken from the jar.

M: One red ball and one green ball are obtained.

Show that P(M\W)=15/28

Find,

(i) P(M and W)

(ii) P(W\M)

(iii) P(WUM)

All the dice and balls are now placed ina single container, and four objects are taken at random, each object being replaced before the next one is taken. Find the probability that one object of each colour is taken.

OK I already proved that P(M\W)=15/28

I used the eqn:P(M\W)={P(MandW)/P(W)}

and P(M)=15/28 P(W)=2/5

For part (i) the ans is 3/14

But I am getting trouble with the rest of questions.

Part (ii) the ans is 5/13 but I dont know how the teacher got that I used the same formula P(W\M)={P(WandM)/P(M)} still not getting through.

Part iii and the last part is also giving problems

Thanks for any help Regards

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