Another question (1 Viewer)

[kooltrainer]

An urn contains 3 red balls and W white balls. Sue draws 2 balls together from the urn. The probability that they have the same colour is 1/2.
Bill adopts a different procedure. He draws one ball from the urn, notes it colour and replaces it. He then draws a second ball from the urn and notes it colour. The probability that both balls have the same colour is now 5/8. Find all possible vaules of W

 

[3unitz]

w/(3+w) . (w-1)/(2+w) + 3/(3+w) . 2/(2+w) = 1/2

2 (w^2 - w + 6) = (3+w)(2+w)

2w^2 - 2w + 12 = 6 + 5w + w^2

w^2 - 7w + 6 = 0

(w - 6) (w - 1) = 0

based on sue's case w=6 or w=1

w/(3+w) . w/(3+w) + 3/(3+w) . 3/(3+w) = 5/8

8 (w^2 + 9) = 5 (3+w)^2

8w^2 + 72 = 45 + 30w + 5w^2

w^2 - 10w + 9 = 0

(w - 9) (w - 1) = 0

based on bills case w=9 or w=1

.'. 1 is the only possible value for w

 

[kooltrainer]

o.. thanks
why did u plus them by the way?
w/(3+w) . (w-1)/(2+w) + 3/(3+w) . 2/(2+w) = 1/2

 

[shaon0]

both these events are seperate (mutually exclusive), i.e. they take out 2 white balls, or 2 red balls hence we use P(A or B) = P(A) + P(B).

Hey do u tutor in maths? i was just wondering.

 

[midifile]

An urn contains 3 red balls and W white balls. Sue draws 2 balls together from the urn. The probability that they have the same colour is 1/2.
Bill adopts a different procedure. He draws one ball from the urn, notes it colour and replaces it. He then draws a second ball from the urn and notes it colour. The probability that both balls have the same colour is now 5/8. Find all possible vaules of W

Whered you get that question from? I think it was in my pretrial (or it was somewhere I just cant remember where - I know ive done it)

 

[shaon0]

i do it makes me warm and very happy

Are you joking? Where do you tutor?

 

[shaon0]

you sure do like asking me questions... i dont even know the name of it, its just a small business in maitland - near newcastle. where do you work shaon0?

lol....i don't work...I was just curious since you are a math freak.

 

[u-borat]

how is this 4unit again?

 

[kooltrainer]

Whered you get that question from? I think it was in my pretrial (or it was somewhere I just cant remember where - I know ive done it)

its from this pheonix book i think.. a collection of really old past papers that my tutor made me do.. like 1980s

 

[midifile]

its from this pheonix book i think.. a collection of really old past papers that my tutor made me do.. like 1980s

Okay. Thanks.

I was just wondering how the answer can be 1, because doesnt it have to be greater than or equal to 2 as you are pulling out 2 balls?

When I did this question I'm sure I wrote w=/=1

 

[midifile]

for sue's case the 2 balls come from the 3 red balls. for bill's case it doesnt matter because the ball is replaced.

Yea. that makes sense

thanks