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

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

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

Source: Beat The GMAT — Problem Solving | Thu Jun 18, 2020 5:39 am

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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

gentvenus: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Tue Oct 01, 2019 5:49 am

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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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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