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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
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GPA: 3.39
A basket contains 5 apples, of which 1 is spoiled and the rest are goo
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12 Dec 2022, 06:22
12 Dec 2022, 06:22
Expert Reply
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Question Stats:
85% (00:55) correct
14% (00:44) wrong based on 7 sessions
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A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the possibility that the 2 apples selected will include the spoiled apple?
A. 1/5
B. 3/10
C. 2/5
D. 1/2
E. 3/5
A. 1/5
B. 3/10
C. 2/5
D. 1/2
E. 3/5
Re: A basket contains 5 apples, of which 1 is spoiled and the rest are goo
[#permalink]
14 Dec 2022, 04:32
14 Dec 2022, 04:32
Expert Reply
Direct combinatorial approach:
\(Probability=\frac{# \ of \ favorable \ outcomes}{total \ # \ of \ outcomes}\):
Favorable outcomes: \(C^1_1*C^1_4\) --> \(C^1_1\) choosing one rotten out of 1 and \(C^1_4\) choosing any for the second apple;
Total # of outcomes: \(C^2_5\), choosing 2 apples out of 5;
\(P=\frac{C^1_1*C^1_4}{C^2_5}=\frac{2}{5}\).
Reverse combinatorial approach:
Let's count the probability of the opposite event and subtract this value from 1. The opposit event will be if out of 2 apples both are good, so \(P=1-\frac{C^2_4}{C^2_5}=\frac{2}{5}\).
Direct probability approach:
\(P=\frac{1}{5}*\frac{4}{4}+\frac{4}{5}*\frac{1}{4}=\frac{2}{5}\): probability of {first apple rotten, second apple good} plus the probability of {first apple good, second apple rotten}.
Reverse probability approach:
Again 1- the probability of the opposite event --> \(P=1-\frac{4}{5}*\frac{3}{4}=\frac{2}{5}\).
Answer: C.
\(Probability=\frac{# \ of \ favorable \ outcomes}{total \ # \ of \ outcomes}\):
Favorable outcomes: \(C^1_1*C^1_4\) --> \(C^1_1\) choosing one rotten out of 1 and \(C^1_4\) choosing any for the second apple;
Total # of outcomes: \(C^2_5\), choosing 2 apples out of 5;
\(P=\frac{C^1_1*C^1_4}{C^2_5}=\frac{2}{5}\).
Reverse combinatorial approach:
Let's count the probability of the opposite event and subtract this value from 1. The opposit event will be if out of 2 apples both are good, so \(P=1-\frac{C^2_4}{C^2_5}=\frac{2}{5}\).
Direct probability approach:
\(P=\frac{1}{5}*\frac{4}{4}+\frac{4}{5}*\frac{1}{4}=\frac{2}{5}\): probability of {first apple rotten, second apple good} plus the probability of {first apple good, second apple rotten}.
Reverse probability approach:
Again 1- the probability of the opposite event --> \(P=1-\frac{4}{5}*\frac{3}{4}=\frac{2}{5}\).
Answer: C.
gmatclubot
Re: A basket contains 5 apples, of which 1 is spoiled and the rest are goo [#permalink]
14 Dec 2022, 04:32
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