In given Example, we added the probabilities of X = 1 and X = 2 because they were mutually exclusive events. For any discrete random variable X, is it always true that X = k and X = m are mutually exclusive events, where k and m represent two values that X can have? Explain.
Example
What is the probability that a family with three children will have at least one child of each sex? In given Example, we defined the random variable X = number of girls in three children. If there is at least one child of each sex, then either the family has one girl and two boys (X = 1) or two girls and one boy (X = 2).
Example
Probability Distribution Function for Number of Girls Suppose that a family has three children and that the probability of a girl is 1/2 for each birth.1 Define the random variable X = number of girls among the three children. Possible values for X are 0, 1, 2, 3. What are the probabilities for these values?