Question

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. 40 %
• B. 50 %
• C. 30 %
• D. 25 %

Answer 1

Answer: (A)

40 %

Use an anagram model to find out the total number of different pairs the magician can pull out of his hat. Since two animals will be in the pair and the other three will not, use the "word" YYNNN.

Thus, there are 10 possible pairs.

Then, list the pairs in which the animals will match. Represent the rabbits with the letters a and b, and the doves with the letters x, y, and z.

Matched Pairs

$R_a{R}_b{D}_x{D}_y$ There are four pairs in which the animals will be a matched set.

$D_x{D}_z{D}_y{D}_z$

Therefore, the probability that the magician will randomly draw a matched set is $\frac{4}{10}=40$%