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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. (Enter your probabilities as fractions.)

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Answer:

The probability distribution for y is 1/3 when y = 0, 1/2 when y = 1 and 1/6 when y = 3

Step-by-step explanation:

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

The probability distribution for y the number of correct matches is;

P(0) = ⅓

P(0) = ⅓P(1) = ½

P(0) = ⅓P(1) = ½P(3) = 1

The children are to match each of three pictures of animals to the word identifying that animal.

Thus, number of possible ways to assign the three words = 3! = 6 ways

Now, This means that there can be;

- 3 complete perfect match which is Y(3)

- 1 perfect match

- 0 perfect match.

Thus;

P(3) = 6/6

P(3) = 1

P(1) = 3/6

P(1) = ½ (because the two that are not correct can be arranged in two ways)

P(0) = 2/6

P(0) = ⅓

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