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A basket contains 5 apples of which 1 is spoiled and the

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New post 13 Apr 2007, 20:43
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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 at random from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple?

1/5
3/10
2/5
1/2
3/5

Why wouldn't it just be something like this: First choice good apple = 4/5 chance...times... 2nd choice bad apple 1/4 = 4/20 = 1/5? Because the order could be switched and say the first choice is the bad apple so = 1/5 then times the second choice for a good apple (4/4) = 4/20 = 1/5...

Am I supposed to add these two scenarios?
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New post 13 Apr 2007, 23:44
Say you have a box: { 4 good apples, 1 bad apple }

Now, in order for you to pick two apples where one of them is spoiled, you have to choose 1 good apple from 4 good and 1 bad apple from 1 bad.

remember the statement 'and' means multiply, so:

we have 4 C 1 * 1 C 1 ways of choosing 1 good and 1 bad = 4 * 1 = 4
The total number of ways to choose two apples out of five is 5 C 2 = 10

So your answer is 4/10 = 2/5

PS. 4C1 = [4! / (4-1)! * 1!] = 4 and similarly with 5C2 = [5! / (5-2)!*2!] = 10
  [#permalink] 13 Apr 2007, 23:44
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A basket contains 5 apples of which 1 is spoiled and the

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