Please,solve this maths question for me.

A bag contains 3 black beads, 5 red beads and 2 green beads.
Gianna takes a bead at random from the bag, records its colour and replaces it.
She does this two more times.
Work out the probability that, of the three beads Gianna takes, exactly two are the same colour

Well the answer is 33/50. It is from past paper.But some statistical stuff was used here, which is kinda irrelevant in separate maths paper. My teacher taught us drawing this probability tree, but still after trying it i didnt get a right answer. Please help.The question worths 5 marks and i from higher past paper

Reply 1

am02

did u get the wrong answer as 11/45??

Reply 2

glance

17

Okay it's been a while since I did probability, but I made a method up and it seemed to come out with the right answer :smile:

If I could remember, I think you may need to use Pascals triangle, but whatever.

Black 3/10
Red   5/10
Green 2/10

1st	2nd	3rd   1stx2ndx3rd  Total sum
3	3	2	18 	54 (this is 18 x 3)
3	2	3
2	3	3

2	2	3	12	36  (12 x 3 etc)
2	3	2
3	2	3

5	2	2	20	60
2	5	2
2	2	5

5	5	3	75	225
5	3	5
3	5	5

5	3	3	45	135
3	3	5
3	5	3

2	5	5 	50	150
5	2	5
5	5	2
			     Total 660/1000
                                      Simplified 330/500 = 33/50

I found all the possible combinations of numbers and in this case, the order does matter.

Reply 3

Chewwy

17

IZZY!

A bag contains 3 black beads, 5 red beads and 2 green beads.
Gianna takes a bead at random from the bag, records its colour and replaces it.
She does this two more times.
Work out the probability that, of the three beads Gianna takes, exactly two are the same colour

Well the answer is 33/50. It is from past paper.But some statistical stuff was used here, which is kinda irrelevant in separate maths paper. My teacher taught us drawing this probability tree, but still after trying it i didnt get a right answer. Please help.The question worths 5 marks and i from higher past paper

lol, when i first saw this, i thought what a horrible question it was. if you were to add up all the combinations you want to find, you'd need to prcess 18 of the 27 possibilities - not a nice job. instead, i realised it would be quicker to take away the other possibilities. so we are left with:

p(2 same colour) = 1 - p(all red, green or black) - p(one of each colour)

= 1 - (3/10)^3 - (5/10)^3 - (2/10)^3 - 6(3/10 x 5/10 x 2/10)

= 0.66

hurrah.

Reply 4

IZZY!

OP

15

thank you.

Please,solve this maths question for me.

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