Ann, Bob and Cathy are students working together on a group project for school. The project involves three tasks, each of which one of the three students will complete: creating a model, interviewing a local expert, and writing a report. No student has the time to complete more than one task, and all three of them have a strong preference for interviewing the local expert. They decide to randomly distribute the three tasks among themselves in a fair manner, such that all three of them have equal odds of completing their preferred task.

After some consideration, they reach for a coin. Bob flips it; if it lands heads, he creates the model; if tails, he interviews a local expert. After he is assigned a task by this method, Cathy flips a coin. If it lands heads, she writes the report; if tails, she is assigned the other remaining task. Ann is then assigned whichever task is left.

What is the probability that Ann is assigned to interview the expert?

An experimental drug is created to reduce the amount of time patients feel sick with the common cold. In clinical trials of people suffering from the common cold, different participants taking the drug experienced symptoms for varying lengths of time. The scientists running the trial rounded each participant’s duration of symptoms to the nearest day, and used this information to develop the following probability distribution:

There were participants. How many of them experienced symptoms for about days?

Three students are playing a game with a fair six-sided die. If an even number is rolled, student A gets a point. If a number less than 4 is rolled, student B gets a point. If a prime number is rolled, student C gets a point. The die will be rolled fifteen times.

Is the game fair? In other words, do all three students have the same odds of getting a point?

An experimental drug is created to reduce the amount of time patients feel sick with the common cold. In clinical trials of people suffering from the common cold, different participants taking the drug experienced symptoms for varying lengths of time. The scientists running the trial rounded each participant’s duration of symptoms to the nearest day, and used this information to develop the following probability distribution:

If the scientists select one of the participants at random, what duration of symptoms can they expect the participant to have experienced?

A spectator at a horse race is deciding which of three high-performing horses to bet on. Each horse’s ranks in past races can be expressed in terms of the following probability distributions:

The spectator wants to bet on the horse with the highest expected rank in its next race. Assuming that past performance is a good predictor of each horse’s performance in its respective next races, which horse should the spectator bet on?

Ann, Bob and Cathy are students working together on a group project for school. The project involves three tasks, each of which one of the three students will complete: creating a model, interviewing a local expert, and writing a report. No student has the time to complete more than one task, and all three of them have a strong preference for interviewing the local expert. They decide to randomly distribute the three tasks among themselves in a fair manner, such that all three of them have equal odds of completing their preferred task.

After some consideration, they reach for a coin. Bob flips it; if it lands heads, he creates the model; if tails, he interviews a local expert. After he is assigned a task by this method, Cathy flips a coin. If it lands heads, she writes the report; if tails, she is assigned the other remaining task. Ann is then assigned whichever task is left. By this method, the group decides that Bob will create the model, Cathy will interview the local expert and Ann will write the report.

Was their chosen method fair?

A spectator at a horse race is deciding which of three high-performing horses to bet on. Each horse’s ranks in past races can be expressed in terms of the following probability distributions:

After some calculation, the spectator identifies and bets on the horse with the highest expected rank in its next race. However, her chosen horse places last in its next race, the other two horses each place first in their next races, and the spectator loses her bet. Why did her strategy fail?

There are two raffles that both support causes that you care about. You have $20, and want to purchase a ticket for the raffle that gives you the best odds of winning.

Raffle A supports a local charity, and has 100 tickets. Each ticket costs $17. One ticket will win a $110 prize, and the remaining tickets will win nothing.

Raffle B supports a national charity, and has 200 tickets. Each ticket costs $19. One ticket will win a $410 prize, and the remaining tickets will win nothing.

Which raffle is a better deal?

A fair coin is flipped 9 times, yielding the following results:

Two students are deciding whether to flip this coin a tenth time, in order to decide which one of them will get to keep the five-dollar bill they found on a sidewalk. Would this be a fair method for making this decision?

There are two raffles that both support causes that you care about. You have $20, and want to purchase a ticket for the raffle that gives you the best odds of winning.

Raffle A supports a local charity, and has 75 tickets. Each ticket costs $15. One ticket will win a $110 prize, and the remaining tickets will win nothing.

Raffle B supports a national charity, and has 100 tickets. Each ticket costs $20. One ticket will win a $410 prize, and the remaining tickets will win nothing.

Which raffle is a better deal?