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# Probability

Former Member
Posts: 1,876,324

**The Mix Honorary Guru**
can someone help me with this question please...

Urn 1 has 2 white balls and 4 red balls.

Urn 2 has 2 white balls and 1 red ball.

a ball is then randomly picked from urn 1 and placed into urn 2

what is the probability of picking a white ball from urn 2?

i think ive done it wrong...

there is 0.33 prob that a white ball will be picked from urn 1

if the white ball then goes into urn 2, there is 0.75 prob that a white ball will be picked from urn 2

from this i then multiplied the 2 together 0.33*0.75 and got 0.2475, but this seems wrong because even if a red ball was moved into urn 2, there would be a 0.5 prob that a white was picked from it.

Thanks

Urn 1 has 2 white balls and 4 red balls.

Urn 2 has 2 white balls and 1 red ball.

a ball is then randomly picked from urn 1 and placed into urn 2

what is the probability of picking a white ball from urn 2?

i think ive done it wrong...

there is 0.33 prob that a white ball will be picked from urn 1

if the white ball then goes into urn 2, there is 0.75 prob that a white ball will be picked from urn 2

from this i then multiplied the 2 together 0.33*0.75 and got 0.2475, but this seems wrong because even if a red ball was moved into urn 2, there would be a 0.5 prob that a white was picked from it.

Thanks

0

## Comments

The Mix Honorary GuruIf that makes sense.

The Mix Honorary GuruThe Mix Honorary Gurulet W be the probability of pulling a known white ball, R be the probability of picking a known red ball and M that of getting the mystery ball

you know that W+R+M=1

does that help any?

The Mix Honorary GuruThe Mix Honorary Guruxsazx thanks for ur post but not really understanding that one, because we are only interested in a white ball being picked from urn1 so the probability of a red ball being picked is irrelevant is it not?

god i wish they would just give us mark schemes!

The Mix Honorary Guruits not irrelevant, otherwise they wouldnt say 'a random ball is picked from urn 1'.

It might just be a badly worded question, but it's not(imo) referring to the probability of them BOTH being white, because a white ball could still be picked from urn 2 even if the random ball from urn 1 was red.

The Mix Honorary Guruprobability of getting RED -

is 1/4 (the one red that started in urn 2) + ( 1/4 (the mystery ball) x 4/6 (the chances of it being red that you picked) )

P(r) = 1/4 + 4/6 x1/4

= 1/4 + 1/6

= 3/12 + 2/12

= 5/12

now, I'll let you work out what the probability of WHITE is for yourself.