Answer to Question #341367 in Statistics and Probability for Thim

Question

A problem in a test given to small children asks them to match each of three pictures

of animals to the word identifying that animal. If a child assigns the three words at

random to the three pictures, find the probability distribution for Y , the number of

correct. matches

Answer 1

We can assign n! number of ways the words to the pictures.

In our question, n = 3, thence n! = 3 * 2 * 1 = 6

The outcome of those six ways for y are:

1 Perfect match

3 one match

2 no matches at all

Therefore, we can confirm that P for y is:

P (0) = 2/6 = 1/3

P (1) = 3/6 = 1/2

P (3) = 1/6

So, the probability distribution for y is 1/3 when y = 0, 1/2 when y = 1 and 1/6 when y = 3.