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# Liberty BUSI 230 Week 3 Exercises 4.1-4.3 Answers Complete Solutions

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### Question 1

Suppose the newspaper states that the probability of rain today is 90%.

What is the complement of the event “rain today”?

What is the probability of the complement? (Enter your answer to two decimal places.)

### Question 2

What is the probability of the following.

(a) An event A that is certain to occur?

(b) An event B that is impossible?

### Question 3

What is the law of large numbers?

If you were using the relative frequency of an event to estimate the probability of the event, would it be better to use 100 trials or 500 trials? Explain.

## STATUS

### Question 4

A recent survey of 1090 U.S. adults selected at random showed that 685 consider the occupation of firefighter to have very great prestige. Estimate the probability (to the nearest hundredth) that a U.S. adult selected at random thinks the occupation of firefighter has very great prestige.

### Question 5

Consider a family with 4 children. Assume the probability that one child is a boy is 0.5 and the probability that one child is a girl is also 0.5, and that the events “boy” and “girl” are independent.

(a) List the equally likely events for the gender of the 4 children, from oldest to youngest. (Let M represent a boy (male) and F represent a girl (female). Select all that apply.)

(b) What is the probability that all 4 children are male? (Enter your answer as a fraction.)

Notice that the complement of the event “all four children are male” is “at least one of the children is female.” Use this information to compute the probability that at least one child is female. (Enter your answer as a fraction.)

### Question 6

Consider the following.

(a) Explain why −0.41 cannot be the probability of some event.

(b) Explain why 1.21 cannot be the probability of some event.

(c) Explain why 120% cannot be the probability of some event.

(d) Can the number 0.56 be the probability of an event? Explain.

### Question 7

Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates? The following data give an indication.

Similarities and Differences in a Random Sample of 375 Married Couples

Suppose that a married couple is selected at random.

(a) Use the data to estimate the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common. (Enter your answers to 2 decimal places.)

(b) Do the probabilities add up to 1? Why should they?

What is the sample space in this problem?

### Question 8

(a) If you roll a single die and count the number of dots on top, what is the sample space of all possible outcomes? Are the outcomes equally likely?

(b) Assign probabilities to the outcomes of the sample space of part (a). (Enter your answers as fractions.)

Do the probabilities add up to 1? Should they add up to 1? Explain.

(c) What is the probability of getting a number less than 6 on a single throw? (Enter your answer as a fraction.)

(d) What is the probability of getting 1 or 2 on a single throw? (Enter your answer as a fraction.)