Explain the difference between experimental probability and theoretical probability. Give an example to show the difference.

After six rolls of a standard die, the experimental probability of rolling a 3 is \frac{2}{6}. What do you expect will happen to the experimental probability if the die is rolled 90 more times? Explain.

Two four-sided dice (each with numbers 1 to 4) are rolled.

a) Use a tree diagram or an organized list to show all the possible outcomes.

b) What is the total number of outcomes?

c) What is the theoretical probability that the sum of the numbers rolled will be 8?

Adele, Dennis, and Marie are siblings. The sum of their ages is 30. Marie is the eldest, and Adele is the youngest. None of the siblings are older than 15 or younger than 5. No two are the same age. List all the combinations of ages they could be.

Shad has 29 cents in his pocket. He could have any combination of pennies, nickels, dimes, and quarters.

a) How many different combinations of coins are possible?

b) How many combinations have fewer nickels than dimes?

Which model would you use to determine each probability?

Two filed-hockey teams are equally matched. What is the probability that the same team will win all of the next four games they play against each other?

Which model would you use to determine each probability?

To qualify to win a trip to Orlando, you must guess the week of the trip. What is the probability that you will qualify?

Which model would you use to determine each probability?

There is a 30% chance of snow on each of the next three days. What is the probability of getting snow on one of these days?

Joan plays on a soccer team. She can usually score on a penalty kick 6 times out of 10. Describe a simulation that you could use to determine the probability of Joan scoring on her next three penalty kicks. Explain why your simulation is appropriate.