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.)

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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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

step-by-step explanation:

the options are kind of confusing. i can tell you what i see going on here when i look at the graph.

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