Probability

Steve is a basketball player on your school’s team. During a game, he gets to take two shots from the free-throw line. On average, Steve makes a shot from the free-throw line half of the time. What is the probability that he will make both shots? 

Al says: “The three possible results are that Steve makes $$0$$ shots, $$1$$ shot, or $$2$$ shots. So, each result has a probability of $${1\over3}$$.”

Use a coin or a number cube to simulate multiple trials of this situation. Then analyze your results and determine if Al’s statement is accurate or not.

Eleven horses enter a race. The first one to pass the finish line wins. Using The Horse Race Board, place counters on the starting squares labeled 2 to 12. Share out the horses so that each person in your group has three or four horses.

How to play:

1. Roll the two dice and add the scores.
2. The horse with that number moves one square forward.
3. Keep rolling the dice.
4. The horse that is first past the finish line wins. 

Questions:

Aimee has two sisters in her family. She thinks the probability of a family having three children who are all born female is $${{{{1\over4}}}}$$ because there can be 0 females, 1 female, 2 females, or 3 females.

Aimee designs a simulation to test her prediction. She flips a coin three times in a row and records the results. She uses heads to represent a female and tails to represent a male. After 10 trials of this simulation, Aimee gets the following results.