Help with probability (1 Viewer)

[PeaceDrummer]

I totally suck when it comes to probablity.. so much that I am stuck on this easy question:

A barrell contains 15 blue marbles and five red marbles. Two marbles are selected from the barrell, the first not being relaced in the barrell before the second is chosen. This experiement is repeated 100 times. On how many occasions (correct to two decimal places) would you expect the two marbles chosen to be:
a) both blue
b) both the same colour
c) different colours
d) selected with at least one being blue

 

[PC]

I totally suck when it comes to probablity.. so much that I am stuck on this easy question:

A barrell contains 15 blue marbles and five red marbles. Two marbles are selected from the barrell, the first not being relaced in the barrell before the second is chosen. This experiement is repeated 100 times. On how many occasions (correct to two decimal places) would you expect the two marbles chosen to be:
a) both blue
b) both the same colour
c) different colours
d) selected with at least one being blue

It's not really an easy question! The best way of tackling this question is to draw a tree diagram and write the probabilities on each of the branches.

P(blue then blue) = 15/20 x 14/19 = 21/38
P(blue then red) = 15/20 x 5/19 = 15/76
P(red then blue) = 5/20 x 15/19 = 15/76
P(red then red) = 5/20 x 4/19 = 1/19

Now we can try each question.

(a) P(both blue) = 21/38 (from above).
So number of times expected = 100 x 21/38 = 55.26

(b) P(both same colour) = 21/38 + 1/19 = 23/38
So number of times expected = 100 x 23/38 = 60.53

(c) P(different colours) = 15/76 + 15/76 = 15/38
So number of times expected = 100 x 15/38 = 39.47

(d) P(at least one blue) = 21/38 + 15/76 + 15/76 = 18/19
So number of times expected = 100 x 18/19 = 94.74

 

[PeaceDrummer]

thankyou! that helped me so much, explained it perfectly! now i know how to do tree diagrams as well, thanks again