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Retired Moderator Joined: 29 Apr 2015
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What is the probability of randomly choosing two cows (one by one) o  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 54% (01:08) correct 46% (00:47) wrong based on 212 sessions

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What is the probability of randomly choosing two cows (one by one) out of all the animals at Old McDonald’s farm?

(1) The ratio of the number of cows to the number of goats at the farm is 5:6.
(2) The only animals at the farm are cows and goats.

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What is the probability of randomly choosing two cows (one by one) o  [#permalink]

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reto wrote:
What is the probability of randomly choosing two cows (one by one) out of all the animals at Old McDonald’s farm?

(1) The ratio of the number of cows to the number of goats at the farm is 5:6.
(2) The only animals at the farm are cows and goats.

Question : Probability of choosing two cows out of All animals = ?

To solve this question all we need is the Number of cows and total Animals

Statement 1: The ratio of the number of cows to the number of goats at the farm is 5:6.
We don't know if there are any other animals in the farm or not. Hence,
NOT SUFFICIENT

Statement 2: The only animals at the farm are cows and goats.
The number of cows and Goats is still unknown. Hence,
NOT SUFFICIENT

Combining the two statements
Cows : Goats = 5:6 and there are no other animals
Case 1: Cows = 5, Goats = 6, i.e. Required Probability = (5/11)*(4/10) = 20/110
Case 2: Cows = 10, Goats = 12, i.e. Required Probability = (10/22)*(9/21) = 90/462
Inconsistent values of Probability. Hence,
NOT SUFFICIENT

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Re: What is the probability of randomly choosing two cows (one by one) o  [#permalink]

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Hi,

If the question would have asked to select 2 cows in one go, we could have done with option - C.

Thanks,
Anchal
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Re: What is the probability of randomly choosing two cows (one by one) o  [#permalink]

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I think even in that case it will be E. Can you please explain how you got C.

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Re: What is the probability of randomly choosing two cows (one by one) o  [#permalink]

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1
I fell for this one. I now realize that had the problem been what is the probability of drawing one cow, then the probability remains the same no matter what is the total number of animals. However, I never thought it would change if we are drawing two animals instead of just one.
sometimes it is worthwhile to just do the problem and see what happens. Very good learning for me.

For example if we had two scenarios --- Scenario 1) 5 cows and 6 goats; Scenario 2) 10 cows and 12 goats
probability of drawing two cows.
Scenario 1) 5/11*4/10
Scenario 2) 10/22*9/21
We see that the first term of the multiplication does not change between the two scenarios. The second term makes all the difference. Now that one cow is taken off, the second term has to be adjusted for total number of goats and cows remaining.
fantastico!
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What is the probability of randomly choosing two cows (one by one) o  [#permalink]

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Can anyone explain why did we choose Case 2: Cows = 10, Goats = 12
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Re: What is the probability of randomly choosing two cows (one by one) o  [#permalink]

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If you're only picking one thing in a probability question, then the actual numbers don't matter - you just need a ratio. For example, if you pick one person from a group, and the ratio of women to men in the group is 2 to 1, then the probability you pick a man is 1/3.

But as soon as you pick two or more things without replacement from a group, then your numbers will matter. Again, if the ratio of women to men is 2 to 1, and you pick two people without replacement, and want to know the probability both are men, then the answer could be zero, if we only have 3 people in total (because then there aren't two men in the group at all that we could even pick), but will not be zero if we have a larger number of people. In this situation, the probability the first selection is a man is 1/3, and the probability the second selection is then also a man will be less than 1/3 (since we've reduced the proportion of men in the group with our first selection), but will get closer and closer to 1/3 the larger the group is.

If instead you make selections with replacement (so your first selection goes back into the original group before you make the next selection) then again, only the ratio matters, since, using the example above, the probability of picking a man would be 1/3 each time.

No real GMAT probability question would be worded the way the question above is, incidentally. A probability question needs to make clear how many selections you're making, and how you're doing it, and this question doesn't even mention that you're selecting exactly two animals.
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GMAT 1: 700 Q49 V37 Re: What is the probability of randomly choosing two cows (one by one) o  [#permalink]

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reto wrote:
What is the probability of randomly choosing two cows (one by one) out of all the animals at Old McDonald’s farm?

(1) The ratio of the number of cows to the number of goats at the farm is 5:6.
(2) The only animals at the farm are cows and goats.

Find: the probability of selecting two cow one by one out of all animals
We need to know total number of cows and all other animals.

s1 cows = 5x goats = 6x, but we don't know are there other animals on the farm? therefore, not sufficient

s2 clearly not sufficient

both: cows = 5x , total animals = 11x

select 2 animals from 11x animals = 11xC2 =$$\frac{11x!}{2!*(11x-2)!}$$

select 2 cows from 5x cows = 5xC2 = $$\frac{5x!}{2!*(5x-2)!}$$

probability =$$\frac{11x!}{2!*(11x-2)!}/\frac{5x!}{2!*(5x-2)!}$$

because we can't cancel x from the equation, this is not sufficient. Answer E.

And if the condition was that cow is replaced after each selection then the answer would be C.

Dear Bunuel chetan2u VeritasKarishma is this approach correct?
_________________ Re: What is the probability of randomly choosing two cows (one by one) o   [#permalink] 18 Feb 2019, 08:57
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