Carol purchased one basket of fruit consisting of 4 Apples and

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pm; Followed by:1 members

Carol purchased one basket of fruit consisting of 4 Apples and

by BTGModeratorVI » Thu May 07, 2020 6:02 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 2021

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Source: Beat The GMAT — Problem Solving | Thu May 07, 2020 6:02 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

Re: Carol purchased one basket of fruit consisting of 4 Apples and

by Brent@GMATPrepNow » Thu May 07, 2020 9:34 am

BTGModeratorVI wrote: ↑
Thu May 07, 2020 6:02 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 2021

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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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

Re: Carol purchased one basket of fruit consisting of 4 Apples and

by swerve » Thu May 07, 2020 11:21 am

BTGModeratorVI wrote: ↑
Thu May 07, 2020 6:02 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 2021

Basket 1: 4 apples, 2 oranges. So total 6 fruits
Basket 2: 3 apples, 5 oranges. So total 8 fruits

Probability of selecting apple from basket 1 and orange from basket 2
\(= \dfrac{4}{6} \cdot \dfrac{5}{8}\)
\(=\dfrac{5}{12}\)

Probability of selecting orange from basket 1 and apple from basket 2
\(=\dfrac{2}{6} \cdot \dfrac{3}{8}\)
\(=\dfrac{1}{8}\)

Since the order of fruit is not specified, we have to consider both these possibilities.

Total probability\(=\dfrac{5}{12}+\dfrac{1}{8} = \dfrac{13}{24}\)

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: Carol purchased one basket of fruit consisting of 4 Apples and

by Scott@TargetTestPrep » Sat May 09, 2020 12:01 pm

BTGModeratorVI wrote: ↑
Thu May 07, 2020 6:02 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 2021

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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