1. Suppose the newspaper states that the probability of rain today is 30%. What is the complement of the event "rain today"? What is the probability of the complement?

2. 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.

3. Consider the experiment of tossing a fair coin 3 times. For each coin, the possible outcomes are heads or tails.

a. List the equally likely events of the sample space for the three tosses.

b.What is the probability that all three coins come up heads? Notice that the complement of the event " 3 heads" is "at least one tail." Use this information to compute the probability that there will be at least one tail.

4. Probability Estimate: Wiggle Your Ears Can you wiggle your ears? Use the students in your statistics class (or a group of friends) to estimate the percentage of people who can wiggle their ears. How can your result be thought of as an estimate for the probability that a person chosen at random can wiggle his or her ears? Comment: National statistics indicate that about 13% of Americans can wiggle their ears (Source: Bernice Kanner, Are You Normal?, St. Martin's Press, New York).

5. Probability Estimate: Raise One Eyebrow Can you raise one eyebrow at a time? Use the students in your statistics class (or a group of friends) to estimate the percentage of people who can raise one eyebrow at a time. How can your result be thought of as an estimate for the probability that a person chosen at random can raise one eyebrow at a time? Comment: National statistics indicate that about 30% of Americans can raise one eyebrow at a time (see source in Problem 15).

6. General: Roll a Die

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). 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 5 on a single throw?

d. What is the probability of getting 5 or 6 on a single throw?

7. Basic Computation: Addition Rule Given P(A)=0.7 and P(B)=0.4 :

a. Can events A and B be mutually exclusive? Explain.

b. If P(Aand B) = 0.2 , compute P(Aor B)

8. Basic Computation: Multiplication Rule Given P(A)=0.7 and P(B)=0.8 :

a. If A and B are independent events, compute P(Aand B) .

b. If P(B|A)=0.9 , compute P(Aand B) .

9. Critical Thinking Consider the following events for a college student selected at random:

A=student is female

B=student is majoring in business

Translate each of the following phrases into symbols.

a. The probability the student is male or is majoring in business

b. The probability a female student is majoring in business

c. The probability a business major is female

d. The probability the student is female and is not majoring in business

e. The probability the student is female and is majoring in business

10.General: Roll Two Dice You roll two fair dice, a green one and a red one.

a. Are the outcomes on the dice independent?

b. Find P(1on green dieand2on red die) .

c. Find P(2on green die and1on red die)

d. Find P[(1on green dieand2on red die)or(2on green dieand1on red die)] .