Probability - help me

[Junior2011]

If one fruit is selected from Basket X with 3 Apples and 5 oranges, and another fruit is selected from Basket Y with 2 apples and 4 oranges, what is the probability of selecting exactly one apple and orange?
How would you attack this question?

In what other ways can the GMAT ask to solve a similar question such as the one above?

I have problems putting the math together to solve this problem. I struggle with probability questions. The Manhattan GMAT strategy guides about Probability are too general, while the questions on the test or the OG Guide are quite specific. In other words for probability questions, I think the Manhattan GMAT strategy is not quite good.
Many thanks,

[sl750]

We can select 1 apple from basket X and 1 orange from basket Y or vice versa

In basket X, we have 3 Apples and 5 Oranges.
Probability of selecting 1 Apple from basket X is 3C1/8C1
and
Probability of selecting 1 Orange from basket Y is 4C1/6C1
Total in this case = 3/8*4/6

Or

Probability of selecting 1 Orange from basket X is 5C1/8C1
and
Probability of selecting 1 Apple from basket Y is 2C1/6C1
Total = 5/8*2/6

Adding the two scenarios

3/8*4/6 + 5/8*2/6 = 1/4 + 5/24 = 11/24

To answer your second question, probably infinite

You can always use this forum for practicing additional problems

[Brent@GMATPrepNow]

If one fruit is selected from Basket X with 3 Apples and 5 oranges, and another fruit is selected from Basket Y with 2 apples and 4 oranges, what is the probability of selecting exactly one apple and orange?
How would you attack this question?

sl750's solution uses counting techniques, and it's solid solution.
Another approach is to apply probability rules.

P(one apple and one orange) = P(apple from X AND orange from Y OR apple from Y AND orange from X)

OR means add
AND means multiply

So, we get:
P(one apple and one orange) = P(apple from X) x P(orange from Y) + P(apple from Y) x P(orange from X)
= (3/8)(4/6) + (2/6)(5/8)
= 12/48 + 10/48
= 22/48
= 11/24

Cheers,
Brent