SOLUTION: Suppose that 20,000 married adults in a country were randomly surveyed as to the number of children they have. The results are compiled and are used as theoretical probabilities. L

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Question 1206559: Suppose that 20,000 married adults in a country were randomly surveyed as to the number of children they have. The results are compiled and are used as theoretical probabilities. Let X = the number of children married people have.
x P(x) xP(x)
0 0.15
1 0.20
2 0.35
3
4 0.10
5 0.05
6 (or more) 0.05
(a) Find the probability that a married adult has three children. (Enter your answer to two decimal places.)
(c) Find the expected value. (Enter your answer to two decimal place.)
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!

X = number of children married people have

x P(x)
0 0.15
1 0.20
2 0.35
3 ????
4 0.10
5 0.05
6 (or more) 0.05

The two key rules for a probability distribution are:
Each P(x) item must be between 0 and 1.
All of the P(x) values must add to 1.
So,
P(0)+P(1)+P(2)+P(3)+P(4)+P(5)+P(6) = 1
0.15+0.20+0.35+P(3)+0.10+0.05+0.05 = 1
0.9+P(3) = 1
P(3) = 1 - 0.9
P(3) = 0.1

The probability a married adult has exactly 3 kids is 0.1

This is what the completed table will look like

x P(x)
0 0.15
1 0.20
2 0.35
3 0.10
4 0.10
5 0.05
6 (or more) 0.05

--------------------------------------------------------------------------

Now to fill out the column labeled x*P(x).
As the name of this column suggests, we'll multiply each paired x and P(x) value.
Eg: 0*0.15 = 0 and 1*0.20 = 0.20

x P(x) x*P(x)
0 0.15 0
1 0.20 0.20
2 0.35 0.70
3 0.10 0.30
4 0.10 0.40
5 0.05 0.25
6 (or more) 0.05 0.30

The "6 (or more)" entry at the bottom is treated simply as x = 6. I wasn't sure how to handle that portion.
Spreadsheet software is recommended. But since the table is fairly small, doing it by hand isn't that bad.

Add up the values in the x*P(x) column to arrive at the expected value 2.15