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Carol purchased one basket of fruit consisting of 4 Apples and 2 Oranges and another basket of fruit

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by BTGModeratorVI » Thu Jun 18, 2020 5:39 am

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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 probability 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

Answer: E
Source: Official guide
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Re: Carol purchased one basket of fruit consisting of 4 Apples and 2 Oranges and another basket of fruit

by Brent@GMATPrepNow » Sat Jun 20, 2020 5:48 am
BTGModeratorVI wrote: ↑
Thu Jun 18, 2020 5:39 am
 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 probability 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

Answer: E
Source: Official guide
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
Brent Hanneson - Creator of GMATPrepNow.com
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Re: Carol purchased one basket of fruit consisting of 4 Apples and 2 Oranges and another basket of fruit

by gentvenus » Sat Jun 20, 2020 8:48 am
= [4/6 x 5/8] + [2/6 x 3/8]
= 13/24
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Re: Carol purchased one basket of fruit consisting of 4 Apples and 2 Oranges and another basket of fruit

by Scott@TargetTestPrep » Sun Jun 21, 2020 4:57 am
BTGModeratorVI wrote: ↑
Thu Jun 18, 2020 5:39 am
 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 probability 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

Answer: E
Source: Official guide
Solution:

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

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