AAPL wrote:GMAT Prep
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
OA A
We are given that from a group of 3 doves and 2 rabbits, 2 animals will be randomly selected. We need to determine the probability that a matched pair will be pulled out of the hat.
In other words, we need to determine:
P(2 doves pulled) + P(2 rabbits pulled)
We can use combinations to determine the number of favorable outcomes (that 2 rabbits or 2 doves are selected) and the total number of outcomes (that 2 animals are selected from 5).
Let's first determine the number of ways we can select 2 doves from 3:
# of ways to select 2 doves from 3 doves: 3C2 = 3
Next let's determine the number of ways we can select 2 rabbits from 2:
# of ways to select 2 rabbits from 2 rabbits: 2C2 = 1
Now we must determine the number of ways to select 2 animals from a total of 5 animals:
5C2 = (5 x 4)/(2 x 1) = 10
Thus, the probability of selecting a matched pair is 3/10 + 1/10 = 4/10 = 2/5.
Alternate Solution:
The two events that satisfy the requirement of getting a matched pair are DD or RR.
The probability of DD is 3/5 x 2/4 = 6/20 =3/10.
The probability of RR is 2/5 x 1/4 = 2/20 = 1/10.
Since DD and RR are mutually exclusive events, the probability that either of these two events happens can be found simply by adding the individual probabilities, which is 3/10 + 1/10 = 4/10 = 2/5.
Answer: A
