STAT 201 Chapter 17: Thinking About Chance

What does it mean if something has a probability of zero?

0 = never occurs Ex: rolling a 6 sided die and getting a 7

What does it mean if something has a probability of 0.5?

0.5 = happens half of the time in a very long series of trials Ex: tossing a coin and getting tails

What does it mean if something has a probability of one?

1 = always occurs Ex: rolling a 6 sided die and getting a number between 1 and 6

Why do some people worry about risks that almost never occur, but ignore other risks that are much more plausible?

1) we feel safer about risks we can control 2) humans are bad at comprehending small probabilities, so we tend to overestimate small risks & underestimate larger risks 3) sometimes probabilities are determined from complex studies (ppl find harder to trust) Ex: very few people would leave a sleeping infant home alone for 10 minutes while they went to run errands, even though the risk of a car crash is higher than the risks the child would face sleeping at home.

What does the Law of Large Numbers say?

in a large number of independent repetitions of a random phenomenon, averages or proportions are likely to become more stable as the number of trials increases

Give an example in which you would rely on a probability found as a long-term proportion from data on many trials.

One time you would rely on a probability found as a long-term proportion from data on many trials is if you wanted to know the probability of rolling a die and getting a 1

Give an example in which you would rely on your own personal probability

One time you would rely on your own personal probability is if you wanted to know the probability of you personally getting in a car crash

When was the first time randomness was studied? When did we begin studying probability theory?

The first time randomness was studied was int he 17th century when gamblers in France wanted to know how they should bet. We began studying probability theory in the 17th century as well.

Random

events that are unpredictable in the short run, but have a pattern in the long run -random if individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of repetitions.

What is the probability of an outcome happening?

number between 0 and 1 describes proportion of times the outcome would occur in a very long series of repetitions

Personal Probability

personal probability of an outcome = number between 0 and 1 that expresses individual's judgement of how likely the outcome is

What do we know about chance behavior in the short run? What do we know about chance behavior in the long run?

short run - do not know anything about chance behavior bc unpredictable long run - chance behavior regular and predictable