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Problem Solving : Probability

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Problem Solving : Probability [#permalink] New post 10 Jul 2010, 00:18
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A
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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 probability that the 2 apples selected will include the spoiled one?

a. 1/5
b. 3/10
c. 2/5
d. 1/2
e. 3/5
[Reveal] Spoiler: OA
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Re: Problem Solving : Probability [#permalink] New post 10 Jul 2010, 00:37
1 spoiled apple. 4 good apples. What is the probability that when two apples are picked, one is spoiled?

No. of ways of picking 2 objects from 5 objects is 5C2 = 10

Favourable situation is one spoiled apple and one good apple.
Do this in two steps. First pick a spoiled apple, and then a good one.
You can pick the spoiled apple in only 1 way.
AND You can pick the good apple in 4 ways
Thus there are 1*4 = 4 ways that one of the two picked apples is spoiled.

Probability = No. of Favourable outcomes / Total number of outcomes

= 4 / 10

= 2 / 5

Pick C
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Re: Problem Solving : Probability [#permalink] New post 10 Jul 2010, 11:37
AbhayPrasanna wrote:
1 spoiled apple. 4 good apples. What is the probability that when two apples are picked, one is spoiled?

No. of ways of picking 2 objects from 5 objects is 5C2 = 10

Favourable situation is one spoiled apple and one good apple.
Do this in two steps. First pick a spoiled apple, and then a good one.
You can pick the spoiled apple in only 1 way.
AND You can pick the good apple in 4 ways
Thus there are 1*4 = 4 ways that one of the two picked apples is spoiled.

Probability = No. of Favourable outcomes / Total number of outcomes

= 4 / 10

= 2 / 5

Pick C


I'm a GMAT newbie, and struggling with my introduction into ordering, combinations, etc. Could you elaborate a bit on the logic here? Thanks in advance.
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Re: Problem Solving : Probability [#permalink] New post 10 Jul 2010, 13:08
there can be two ways in which one can select a spoiled apple and a good apple.

1. you pick the spoiled one first and the good one later..

Prob of picking bad one = 1/5 (one bad apple)
Prob of picking a good one from the remaining 4 good apples (4/4 =1)

therefore the total prob for case 1 = i/5 * 1 = 1/5

2. Picking the good one first and spoiled one later

Prob of picking a good one = 4/5
Prob of picking bad one rom the remaining 4 apples = 1/4

Total prob = 4/5*1/4 = 1/5

Total prob = porb1 + prob2 = 1/5+1/5 = 2/5


hope this helps
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Re: Problem Solving : Probability [#permalink] New post 10 Jul 2010, 21:02
We are talking about "simultaneously".
2 possibilities: spoiled, normal or
normal spoil.
Spoiled, normal = 1/5*4/4 = 1/5
Normal, spoiled = 4/4*1/5 = 1/5
But we take 2 apples at the same time, so we multiply the result on 2 = 1/5*2 = 2/5 (C)
Re: Problem Solving : Probability   [#permalink] 10 Jul 2010, 21:02
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