Exam 14: Understanding Probability and Long-Term Expectations

Tell whether the following statement is correct; if it is not correct, explain the problem."If the probability of a single birth resulting in a boy is .51, then the probability of it resulting in a girl is also .51."

Give two examples of ways that we speak about probability in our every day lives.

For Questions use the following narrative: Narrative: Shaking hands Suppose the chances of picking up a cold from someone by shaking hands with them is .01 (assuming you don't know whether they have a cold or not), and that each encounter you have is independent of another. -{Shaking hands narrative} Explain, using probability, why your chance of not getting a cold in a given day decreases as the number of handshakes you make increases?

Give an example of a situation where you have to use the personal probability interpretation of a probability (vs.the relative frequency interpretation).

Which of the following is an example of using the personal probability interpretation of probability?

What is one caution you should observe when encountering personal probabilities that are reported in the media?

Suppose Bob and Mary are each trying to determine whether or not a coin is fair (that is, the coin has an equal chance of landing heads up or tails up).Bob flips the coin 100 times and finds that it lands heads up 80 times.Mary flips the coin 1,000 times and finds that it lands heads up 800 times.Compare the relative frequencies in each case and discuss who (if anyone) has stronger evidence that the coin is unfair.

Give an example where you can use the relative-frequency approach to determine a probability.

The airlines routinely report their on-time flight percentages, which can be interpreted as probabilities.What method of finding probabilities was most likely used in determining this?

For Questions use the following narrative Narrative: Taxes Suppose you have a taxing policy where 60% of the population pays $10,000 per year in taxes per person, and the other 40% pays $100 per year in taxes per person. -{Taxes narrative} Explain how the expected value can be misleading if it is interpreted by someone as the amount of taxes they will have to pay in a given year.

Using the relative frequency approach, we can define the probability of any specific outcome as the __________ of times it occurs over the long run.

Describe a situation where you can't use the relative frequency approach to interpret probability.

Which of the following describes an example of an expected value in a lottery situation?

For Questions , use the following narrative: Narrative: Instant lotto Suppose an "Instant Lotto" ticket costs $5, and the chances of winning the $500 prize are 1/10,000.There are no other prizes. -{Instant lotto narrative} What is your expected value for this game for each ticket you buy?

Suppose the chance that your plane will depart and arrive on time in the same trip is 90%.The chance that your plane will depart on time on any given trip is __________ 90%.(Choose one: at most, equal to, or at least, and fill in the blank.)

Which probability is the smallest?

Suppose the outcomes of births within a given family are independent of each other, and a couple has already had four boys.Which of the following best describes the probability that their next baby will be a girl?

For Questions use the following narrative: Narrative: Shaking hands Suppose the chances of picking up a cold from someone by shaking hands with them is .01 (assuming you don't know whether they have a cold or not), and that each encounter you have is independent of another. -{Shaking hands narrative}.Suppose you shake hands with 5 people in a given day.What is the probability that you don't pick up a cold from any of these people?

The __________ represents the average value of any measurement over the long run.

Which of the following is a true probability?