
Concept explainers
To calculate: The probability distribution for the random variable X, if there is a couple that has two children and X is a number of boys, assuming that the chances of a child being a boy or a girl are same.

Answer to Problem 1RE
Solution:
The probability distribution for a number of boys is:
Explanation of Solution
Given Information:
There is a couple that has two children and X is a number of boys, assuming that the chances of a child being a boy or a girl are the same.
Formula Used:
If n is the number of trials and X is the number of successes, then the probability for a particular value of X is given by:
Calculation:
Consider the number of children
Evaluate the probability of success which is the probability of a boy.
Evaluate the probability of failure which is the probability of a girl.
Possible values of X being a boy child are
Now estimate the probability of each value of n by applying the formula
Evaluate the probability
Evaluate the probability
Evaluate the probability
The probability distribution for the number of boys is,
Graph:
The steps to draw the histogram of the binomial distribution is
Step 1: Place x values on the horizontal axis.
Step2. Place the value of probability
Step3. Construct a bar over each value of x extending from
Draw the graph of the binomial distribution as follows:
Interpretation:
The histogram of the probability distribution of a boy child out of two children where the probability of selecting a girl or boy child is equal.
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