xALIx wrote:

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

We can also solve the question using

counting methodsTo begin, P(matched pair) = (

# of ways to get a matched pair)/(

# of ways to select 2 animals)

As always, begin with the

denominator.

# of ways to select 2 animalsTo count this, we'll treat each animal as different.

We'll take the task of selecting 2 animals and break it into stages.

Stage 1: Select the 1st animal. There are 5 animals, so this stage can be accomplished in 5 ways.

Stage 2: Select the 2nd animal. There are now 4 animals remaining, so this stage can be accomplished in 4 ways.

So, the total number of ways to select 2 animals is (5)(4), which equals

20Now the

numerator.

# of ways to get a matched pair

We need to consider two cases.

Case 1: select 2 doves.

In how many different ways can this occur?

Well, we'll take the task of selecting 2 doves and break it into stages.

Stage 1: Select the 1st dove. There are 3 doves, so this stage can be accomplished in 3 ways.

Stage 2: Select the 2nd dove. There are now 2 doves remaining, so this stage can be accomplished in 2 ways.

So, the total number of ways to select 2 doves is (3)(2), which equals

6Case 2: select 2 rabbits.

In how many different ways can this occur?

Well, we'll take the task of selecting 2 rabbits and break it into stages.

Stage 1: Select the 1st rabbit. There are 2 rabbits, so this stage can be accomplished in 2 ways.

Stage 2: Select the 2nd rabbit. There is now 1 rabbit remaining, so this stage can be accomplished in 1 ways.

So, the TOTAL number of ways to select 2 rabbits is (2)(1), which equals

2Put it all together to get:

P(matched pair) = (

6+2)/(

20)

=

8/

20= 2/5

= A

Cheers,

Brent

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