Probability help?

[Andiio]

Two bowls each contain 8 pieces of fruit. In bowl 'A' there are five oranges and three apples, in bowl B there is one orange and seven apples.

One bowl is chosen at random and from it 2 pieces of fruit are chosen at random, the first piece of fruit being replaced before the second is chosen. if both pieces of fruit are apples, find the probability that bowl 'A' was chosen.

Thanks in advance!

[Aqualim]

I'm gonna suggest setting up two tree diagrams, one for bowl A and one for Bowl B, although there is probably an easier to do this.

[UncleXxx]

Sorry if it's too messy.

Assuming that both bowls have an equal chance of being selected.

SOrry if i'm wrong.

[Andiio]

yeah that's wat i thought at first, but isn't it supposed to be A intersection B, not A union B in the numerator of the conditional. prob formula? I was thinking of doing that but then I got stuck on calculating the intersection :/

oh wait they are independent events.. .hmm

[UncleXxx]

Sorry my bad, that should have been intersection. Other than that, the working out should be fine. I think =]

(fixed the drawing)

[Andiio]

Mm yep, haha
So wait, are the bowls and apples independent events? B/c if you pick the other bowl then you get a diff amount of apples :/

[UncleXxx]

I thought the probablity of an apple being picked depends on which bowl it is. If i picked bowl A the probability of picking an apple will be different to the probability of picking an apple in bowl B.

Hope that makes sense

[Andiio]

Oh yep, so they are necessarily independent events 'INSIDE' the bowls? But they aren't outside? (If what I just said makes sense haha)

[UncleXxx]

Sorry, i don't really understand that. You'll probably need someone else to clear things up for you. That's all the help i could provide. Gl =]