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wishmasterdj
Joined: 04 May 2016
Last visit: 25 Oct 2021
Posts: 94
Own Kudos:
Given Kudos: 10
Location: India
Schools: ISB '18 (A)
GMAT 1: 700 Q48 V37
GPA: 3.2
27 Feb 2021, 05:37
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itsabhishekgupta
Can we interpret in the following way?
It shouldnt matter whichever animal he takes out in the first time - implies probability is 1.
What matters really is the second animal that he chooses.
As he has already chose 1 animal, so the remaining animals are 4. Hence whichever animal he pulls out will make a matched pair with the first chosen animal. Therefore the probability should be 1/4 or 25%
Whats wrong with this approach?
It shouldnt matter whichever animal he takes out in the first time - implies probability is 1.
What matters really is the second animal that he chooses.
As he has already chose 1 animal, so the remaining animals are 4. Hence whichever animal he pulls out will make a matched pair with the first chosen animal. Therefore the probability should be 1/4 or 25%
Whats wrong with this approach?
I think I understand why you may think this, especially if you have done similar questions like these, but with one subtle but important difference - the things here are different, with different respective quantities.
e.g. if this was say, 5 pairs of ducks (Male-female), you could then use your approach.
P(of choosing first) = 1 and then the other one to compare the pair would be 1/9, so total would be 1*1/9 = 1/9
Here it does not matter which couple you pick it from, unlike the one in the question.
However, since these are different things in the given question, their starting cases cant be considered as the same (3 vs 2) and thus you have to take each one as a standalone case (DD and RR).
Hope this helps resolve the confusion
30 Mar 2024, 06:26
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I initially used to find these type of questions very hard even though they are classified as EASY according to GMAT standards.
I will tell you my approach
3 Doves and 2 Rabbits
Total Animals = 5
Q - What is the P of getting a pair ?
Ans
Imagine you are a magician and you are taking out these animals from a box, which has 5 of these animals.
Case 1: 2 Rabbits
1. P ( of selecting 1 rabbit) = 1/5 easy ?
2. P( of selecting another rabbit) = 1/4 ( 4 because 1 rabbit is already out )
Therefore, the total Probability of taking out a rabbit pair = 1/5 * 1/4
Case 2: 2 Doves
1. P ( of selecting 1 dove) = 3/5 easy ?
2. P( of selecting another dove) = 2/4 ( 4 because 1 dove is already out )
Therefore, the total Probability of taking out a dove pair = 3/5 * 2/4
Now comes the tricky part.
Question -what is the chance that he will have a matched pair?
As a magician when you are performing this trick you will either take out a pair of dove or a pair Rabbit.
When the situation has OR you have to add the probabilities
therefore if you add. 1/5 * 1/4 + 3/5 * 2/4
You will get A as answer which is 2/5
I will tell you my approach
3 Doves and 2 Rabbits
Total Animals = 5
Q - What is the P of getting a pair ?
Ans
Imagine you are a magician and you are taking out these animals from a box, which has 5 of these animals.
Case 1: 2 Rabbits
1. P ( of selecting 1 rabbit) = 1/5 easy ?
2. P( of selecting another rabbit) = 1/4 ( 4 because 1 rabbit is already out )
Therefore, the total Probability of taking out a rabbit pair = 1/5 * 1/4
Case 2: 2 Doves
1. P ( of selecting 1 dove) = 3/5 easy ?
2. P( of selecting another dove) = 2/4 ( 4 because 1 dove is already out )
Therefore, the total Probability of taking out a dove pair = 3/5 * 2/4
Now comes the tricky part.
Question -what is the chance that he will have a matched pair?
As a magician when you are performing this trick you will either take out a pair of dove or a pair Rabbit.
When the situation has OR you have to add the probabilities
therefore if you add. 1/5 * 1/4 + 3/5 * 2/4
You will get A as answer which is 2/5
21 May 2025, 07:45
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Answer: A. 2/5
You will be picking 2 animals from 5 hats so 5C2 = 10. You might pick 2 rabbits out of the 2 rabbits so 2C2 = 1. You might also pick 2 doves out of the 3 doves so 3C2 = 3. Both count as a matched pair so (2C2 + 3C2)/(5C2) = 2/5.
You will be picking 2 animals from 5 hats so 5C2 = 10. You might pick 2 rabbits out of the 2 rabbits so 2C2 = 1. You might also pick 2 doves out of the 3 doves so 3C2 = 3. Both count as a matched pair so (2C2 + 3C2)/(5C2) = 2/5.
xALIx
A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance that he will have a matched pair?
A. 2/5
B. 3/5
C. 1/5
D. 1/2
E. 7/5
A. 2/5
B. 3/5
C. 1/5
D. 1/2
E. 7/5
