# Estimating Probabilities Through Repeated Experiments

Warmup

Locate and label these numbers on the number line by dragging the points.

Activity #1

Probability Game.

This applet displays a random number from 1 to 6, like a number cube.. • Choose any two numbers from 1 to 6.
• Record them in the boxes in the center of the applet.
• Click the Roll button for 10 rolls and answer the questions.

Mai plays a game in which she only wins if she rolls a 1 or a 2 with a standard number cube.

(1.) List the outcomes in the sample space for rolling the number cube.

(2.) What is the probability Mai will win the game? Explain your reasoning.

(3.) What appears to be happening with the points on the graph?

(4.) After 10 rolls, what fraction of the total rolls were a win?

(5.) How close is this fraction to the probability that Mai will win?

(6.) Roll the number cube 10 more times. Record your results in the table and on the graph from earlier. After 20 rolls, what fraction of the total rolls were a win?

(7.) How close is this fraction to the probability that Mai will win?

Activity #2

`Explore Experimental Probability.` • Press to make the spinner land on a random color. The Spinner will calculate the experimental probability after each trial.
• Press to start over.

(1.) What do you think the probability should be for each color, before using the spinner?

(2.) How does the experimental probability compare to the anticipated probability?

Challenge #1

A spinner has four equal sections, with one letter from the word “MATH” in each section.

(1.) You spin the spinner 20 times. About how many times do you expect it will land on A?

(2.) You spin the spinner 80 times. About how many times do you expect it will land on something other than A? Explain your reasoning.

Challenge #2

A spinner is spun 40 times for a game. Here is a graph showing the fraction of games that are wins under some conditions.

(2.) Which event is more likely: rolling a standard number cube and getting an even number, or flipping a coin and having it land heads up?

Challenge #3

A carnival game has 160 rubber ducks floating in a pool. The person playing the game takes out one duck and looks at it.

• If there’s a red mark on the bottom of the duck, the person wins a small prize.
• If there’s a blue mark on the bottom of the duck, the person wins a large prize.
• Many ducks do not have a mark.

After 50 people have played the game, only 3 of them have won a small prize, and none of them have won a large prize.

(1.) Estimate the number of the 160 ducks that you think have red marks on the bottom.

(2.) Estimate the number of ducks you think have blue marks. Explain your reasoning.

Quiz Time