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GMAT Club World Cup 2022 (DAY 7): Ronaldo puts an orange, an apple and

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Re: GMAT Club World Cup 2022 (DAY 7): Ronaldo puts an orange, an apple and [#permalink] New post   20 Jul 2022, 05:12
Ronaldo puts an orange, an apple and a banana in each of his 4 children's lunch boxes. The 5th child runs into the kitchen and randomly grabs one fruit from each of the 4 bags. What is the probability that she got exactly 2 different types of fruit ?

(A) 1/3
(B) 4/9
(C) 13/27 - correct
(D) 14/27
(E) 16/27
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Re: GMAT Club World Cup 2022 (DAY 7): Ronaldo puts an orange, an apple and [#permalink] New post   20 Jul 2022, 05:12
Ronaldo puts an orange, an apple and a banana in each of his 4 children's lunch boxes. The 5th child runs into the kitchen and randomly grabs one fruit from each of the 4 bags. What is the probability that she got exactly 2 different types of fruit ?

(A) 1/3
(B) 4/9
(C) 13/27
(D) 14/27
(E) 16/27

Let Apple = A, Orange = O & Banana = B

Now, Total ways of picking (he can pick any of orange or apple or banana from each of the boxes = 3 * 3 * 3 * 3 = 81

Favourable ways = 3 arrangements possible for picking exactly 2 different types of fruits = (A+B) or (A+O) or (B+O)
= 3 * 2 * (4C2 * 2C2)
(2 to account for 2 ways of picking amongst A+B and B+A for a particular picking amongst lunch boxes)
= 36 ways

Hence, Probability = 36/81
= 4/9


(B) is the correct answer
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Re: GMAT Club World Cup 2022 (DAY 7): Ronaldo puts an orange, an apple and [#permalink] New post   20 Jul 2022, 05:40
Answer is C

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Re: GMAT Club World Cup 2022 (DAY 7): Ronaldo puts an orange, an apple and [#permalink] New post   Updated on: 25 Oct 2022, 03:53
Total ways=3^4=81
Exactly 2 out of 3 can be chosen in 3C2 ways.
These 2 types of fruits can be chosen in 2^4=16 ways
However, it may be possible that same fruit gets chosen from all the 4 bags. So 2 ways to be deducted from 16.
Prob=3*14/81=14/27
Answer is D.

Originally posted by Kushchokhani on 20 Jul 2022, 05:44.
Last edited by Kushchokhani on 25 Oct 2022, 03:53, edited 1 time in total.
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Re: GMAT Club World Cup 2022 (DAY 7): Ronaldo puts an orange, an apple and [#permalink] New post   20 Jul 2022, 07:34
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The 5th child can draw the fruits in overall 3 x 3 x 3 x 3 combinations = 3^4 = 81 combinations
Now the combinations for exactly 2 different types of fruit can be
All combinations of AAOO, AABB, OOBB = 4!/2! = 6 for each
All combinations of AOOO, ABBB, OBBB, OAAA, BAAA, BOOO = 4!/3! = 4 for each

Total probability

3*(6/81) + 6*(4/81) = 6/27 + 8/27 = 14/27

IMHO Option D
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Re: GMAT Club World Cup 2022 (DAY 7): Ronaldo puts an orange, an apple and [#permalink] New post   20 Jul 2022, 07:44
Bunuel wrote:
Ronaldo puts an orange, an apple and a banana in each of his 4 children's lunch boxes. The 5th child runs into the kitchen and randomly grabs one fruit from each of the 4 bags. What is the probability that she got exactly 2 different types of fruit ?

(A) 1/3
(B) 4/9
(C) 13/27
(D) 14/27
(E) 16/27

 


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Total outcomes = 3*3*3*3 = 81
Exactly 2 different types of fruits => 2A,2O OR 2A,2B OR 2B,2O
Possible outcomes for each = 4c2 * 2! = 12
Possible outcomes overall = 12 + 12 + 12 = 36

Probability = 36/81 = 4/9

Answer - B
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Re: GMAT Club World Cup 2022 (DAY 7): Ronaldo puts an orange, an apple and [#permalink] New post   20 Jul 2022, 07:45
Hello everyone

The answer is C. Guessed.
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Re: GMAT Club World Cup 2022 (DAY 7): Ronaldo puts an orange, an apple and [#permalink] New post   20 Jul 2022, 07:59
Bunuel wrote:
Ronaldo puts an orange, an apple and a banana in each of his 4 children's lunch boxes. The 5th child runs into the kitchen and randomly grabs one fruit from each of the 4 bags. What is the probability that she got exactly 2 different types of fruit ?

(A) 1/3
(B) 4/9
(C) 13/27
(D) 14/27
(E) 16/27

 


This question was provided by GMAT Club
for the GMAT Club World Cup Competition

Compete, Get Better, Win prizes and more

 


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Re: GMAT Club World Cup 2022 (DAY 7): Ronaldo puts an orange, an apple and [#permalink] New post   03 Apr 2024, 07:39
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Re: GMAT Club World Cup 2022 (DAY 7): Ronaldo puts an orange, an apple and [#permalink]
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