Suppose that A and B are two events. Write expressions involving unions, intersections, and complements that describe the following: At least one occurs.

Suppose a family contains two children of different ages, and we are interested in the gender of these children. Let F denote that a child is female and M that the child is male and let a pair such as F M denote that the older child is female and the younger is male. There are four points in the set S of possible observations:

$$S = \{ F F , F M , M F , M M \}$$

. Let A denote the subset of possibilities containing no males; B, the subset containing two males; and C, the subset containing at least one male. List the elements of

$$A,\ B,\ C,\ \ A\ \cap B,\ A\ \cup B,\ A\ \cap C,\ A\ \cup C,\ B\cap C,\ B\cup C,\ and\ C\ \cap\overline{B}$$

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The proportions of blood phenotypes, A, B, AB, and O, in the population of all Caucasians in the United States are approximately .41, .10, .04, and .45, respectively. A single Caucasian is chosen at random from the population. Make use of the information given above to assign probabilities to each of the simple events.

The proportions of blood phenotypes, A, B, AB, and O, in the population of all Caucasians in the United States are approximately .41, .10, .04, and .45, respectively. A single Caucasian is chosen at random from the population. List the sample space for this experiment.

The proportions of blood phenotypes, A, B, AB, and O, in the population of all Caucasians in the United States are approximately .41, .10, .04, and .45, respectively. A single Caucasian is chosen at random from the population. What is the probability that the person chosen at random has either type A or type AB blood?

Suppose two balanced coins are tossed and the upper faces are observed. From your answer to part (c), find

$$P ( A ) , P ( B ) , P ( A \cap B ) , P ( A \cup B ) , \text { and } P ( \overline { A } \cup B )$$