Question

Expected value is 1.5

8. Construct a counting tree to list the possible outcomes of a 3-child familly. Verify that the expected value (of having 0,1,2 or 3 boys) is 1.5.
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Answer 1

To construct a counting tree for a 3-child family, write down all possible outcomes for each child and calculate their average value. The expected value for having 0, 1, 2, or 3 boys is 1.5.

Step-by-step explanation:

To construct a counting tree for a 3-child family, you start with the first child and write down all possible outcomes. For each outcome, you move on to the second child and write down the possible outcomes again. Finally, you move on to the third child and write down the outcomes once more. This will give you a complete list of all possible outcomes for a 3-child family.

Let's suppose that having a boy is represented by the number 1 and having a girl is represented by the number 0. The possible outcomes for each child are:

1. Child 1: {0, 1}
2. Child 2: {0, 1}
3. Child 3: {0, 1}

The total number of possible outcomes is found by multiplying the number of outcomes for each child together: 2 x 2 x 2 = 8.

To verify that the expected value is 1.5, we assign a value of 1 to each boy and a value of 0 to each girl. Then, we calculate the average value of all possible outcomes, which gives us the expected value. The expected value is calculated as follows:

(0 + 1 + 2 + 3) / 8 = 6 / 8 = 1.5

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