Chapter 5: Probability and Random Variables

In Exercises 5.16-5.26, express your probability answers as a decimal rounded to three places.

Coin Tossing. A balanced dime is tossed three times. The possible outcomes can be represented as follows.

Here, for example. HHT means that the first two tosses come up heads and the third tails. Find the probability that

(a) exactly two of the three tosses come up heads.

(b) the last two tosses come up tails.

(c) all three tosses come up the same.

(d) the second toss comes up heads.

Housing Units. Refer to Exercise 5.19.

(a) Which, if any, of the events in parts (a)-(c) are certain? impossible?

(b). Determine the probability of each event identified in part (a).

Family Size.Refer to Exercise 5.24.

(a) Which, if any, of the events in parts (a)-(e) are certain? impossible?

(b) Determine the probability of each event identified in part (a).

Gender and Handedness. This problem requires that you first obtain the gender and handedness of each student in your class. Subsequently, determine the probability that a randomly selected student in your class is

(a). female.

(b) left-handed.

(c) female and left-handed.

(d) neither female nor left-handed.

What is the difference between selecting a member at random from a finite population and taking a simple random sample of size 1?

The probability is 0.314 that the gestation period of a woman will exceed 9 months. In 4000 human gestation periods, roughly how many will exceed 9 months?

The probability is 0.667 that the favorite in a horse race will finish in the money (first, second, or third place). In 500 horse races, roughly how many times will the favorite finish in the money?

U.S. Governors. In 2013, according to the National Governors Association, 30 of the 50 state governors were Republicans. Suppose that on each day of 2013, one U.S. state governor was randomly selected to read the invocation on a popular radio program. On approximately how many of those days should we expect that a Republican was chosen?

Explain what is wrong with the following argument: When two balanced dice are rolled, the sum of the dice can be 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12, giving 11 possibilities. Therefore the probability is $\frac{1}{11}$ that the sum is 12.

Bilingual and Trilingual. At a certain university in the United States, 62 % of the students are at least bilingual - speaking English and at least one other language. Of these students, 80 % speak Spanish and, of the 80 % who speak Spanish, 10 % also speak French. Determine the probability that a randomly selected student at this university

(a) does not speak Spanish.

(b) speaks Spanish and French.