Question

Let

X
X represents the number of children in a household. a) Complete the following probability distribution of
�
X : b) What is the probability that a random

Answer 1

The random variable X is defined as the number of children in a randomly selected household. Values X may include are nonnegative integers. To find the probability of no children, we use the probability distribution function for X=0.

Step-by-step explanation:

To address the questions regarding the random variable X, which represents the number of children in a household, we should proceed as follows:

Define the random variable X

In words, the random variable X is defined as the number of children in a randomly selected household.

List the values that X may take on

The values that X may take on could be 0, 1, 2, 3, etc., depending on the maximum number of children considered for this distribution.

Give the distribution of X

The distribution of X would be provided as a probability distribution function, which includes the probability of each count of children per household.

Find the probability of no children

To find the probability that a household has no children, we would look at the value assigned to X=0 in the probability distribution function.

Answer 2

a) X | P(X)

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

0 | 0.15

1 | 0.25

2 | 0.4

3 | 0.2

b) The probability that a random household selected will have three or more children is 0.2.

Step-by-step explanation:

For part (a), completing the probability distribution, the sum of all probabilities must equal 1. Given the probabilities for households with 0, 1, and 2 children (0.15, 0.25, and 0.4 respectively), the remaining probability for households with 3 or more children can be calculated by subtracting the sum of the known probabilities from 1. Thus, the probability for households with 3 children (or more) is 0.2, completing the distribution.

Part (b) asks for the probability of a household having three or more children. This is obtained by combining the probabilities for households with 3, 4, or more children.

In this case, the probability for 3 children is 0.2. As it stands for three or more children collectively, this single probability represents the likelihood of a randomly selected household having three or more children, fulfilling the requirement of the question.

Here is complete question;

"Let X represent the number of children in a household.

a) Complete the following probability distribution of X:

X | P(X)

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

0 | 0.15

1 | 0.25

2 | 0.4

3 | ?

b) What is the probability that a random household selected will have three or more children?"