Carol purchased one basket of fruit consisting of 4 Apples and

Question

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

Brent@GMATPrepNow · Answer

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

swerve · Answer

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$=\dfrac{5}{12}+\dfrac{1}{8} = \dfrac{13}{24}$

Scott@TargetTestPrep · Answer

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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