A magician has five animals in his magic hat: 3 doves and 2

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

Let's apply probability rules

First notice that, to get a matched pair, we can select 2 doves or 2 rabbits.

So, P(matched pair) = P(1st pick is rabbit AND 2nd pick is rabbit OR 1st pick is dove AND 2nd pick is dove)

We can now apply our AND and OR rules to get:
P(matched pair) = [P(1st pick is rabbit) x P(2nd pick is rabbit)] + [P(1st pick is dove) x P(2nd pick is dove)]
So, P(matched pair) = (3/5 x 2/4) + (2/5 x 1/4)
We get: 2/5 (or 0.4)

Answer: A


Cheers,
Brent

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