OG: Carol purchased one basket of fruit consisting of 4 apples and 2 oranges

[AbeNeedsAnswers]

Carol purchased one basket of fruit consisting of 4 apples and 2 oranges and another basket of fruit consisting of 3 apples and 5 oranges. Carol is to select one piece of fruit at random from each of the two baskets. What is the possibility that one of the two pieces of fruit selected will be an apple and the other will be an orange?

A. 1/4
B. 1/2
C. 1/24
D. 5/24
E. 13/24

E

[Brent@GMATPrepNow]

Carol purchased one basket of fruit consisting of 4 apples and 2 oranges and another basket of fruit consisting of 3 apples and 5 oranges. Carol is to select one piece of fruit at random from each of the two baskets. What is the possibility that one of the two pieces of fruit selected will be an apple and the other will be an orange?

A. 1/4
B. 1/2
C. 1/24
D. 5/24
E. 13/24

E

Let's name the baskets!
Basket A has 4 Apples and 2 Oranges
Basket B has 3 Apples and 5 Oranges

P(1 of each type) = P(select apple from basket A AND orange from basket B OR select orange from basket A AND apple from basket B)
= [P(apple from basket A) x P(orange from basket B)] + [P(orange from basket A) x P(apple from basket B)]
= [4/6 x 5/8] + [2/6 x 3/8]
= 20/48 + 6/48
= 26/48
= 13/24

Answer: E

Cheers,
Brent

[Scott@TargetTestPrep]

Carol purchased one basket of fruit consisting of 4 apples and 2 oranges and another basket of fruit consisting of 3 apples and 5 oranges. Carol is to select one piece of fruit at random from each of the two baskets. What is the possibility that one of the two pieces of fruit selected will be an apple and the other will be an orange?

A. 1/4
B. 1/2
C. 1/24
D. 5/24
E. 13/24

E

The probability of selecting an orange from the first basket and an apple from the second basket is:

2/6 x 3/8 = 1/3 x 3/8 = 3/24

The probability of selecting an apple from the first basket and an orange from the second basket is:

4/6 x 5/8 = 2/3 x 5/8 = 10/24

Thus, the overall probability is 3/24 + 10/24 = 13/24.

Answer: E

[pyaasa]

Basket 1 - 4 A, 2 O; Basket 2- 3 A, 5 O
Probability = No of fav outcomes/Total no of outcomes
Fav Outcomes = 4C1*5C1+2C1*3C1 (Selecting 1 A &(AND 1O from B1 OR 1 O & 1 A from B2)


AND means multiplication and OR means addition

Total outcomes - 6C1*8C1 (Selecting 1 item from B1 AND Selecting one item from B2 - Question mentions that 1 item is picked from either basket at a time)

Probablity =20+6/48=26/48=13/24