4.1: What is probability

(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?

1, 2, 3, 4, 5, 6; equally likely

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

A probability must be between zero and one.

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

A probability must be between zero and one.

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

A probability must be between zero and one.

What is the law of large numbers?

As the sample size increases, the relative frequency of outcomes gets closer to the theoretical probability of the outcome.

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 (Source: Bernice Kanner, Are You Normal?, St. Martin's Press, New York).

The resulting relative frequency can be used as an estimate of the true probability of all Americans who can raise one eyebrow.

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

Yes, it is a number between 0 and 1.

1, 2, 3, 4, 5, 6; equally likely

outcome I Probability 1 1/6 2 1/6 3 1/6 4 1/6 5 1/6 6 1/6