Experimental Probability of Simple Events

Warm Up

Experimental probability can be used to approximate the probability of an event. A simple event is an event for which only one outcome exists. A simulation is a model of an experiment that would be difficult or inconvenient to actually perform. It can be used to find an experimental probability and make a prediction. To find the experimental probability of a simple event repeat an experiment several times. Write the ratio of the number of successful outcomes to the total number of times the experiment was conducted.

Experimental probability is always based on events that have already occurred. Determining the experimental probability of an event can, and will, yield any number of outcomes. That is why experimental probability is only an estimate. The total of the experimental probabilities should always be equal to 1 since the sum of the results in the numerators should equal the total number of trials in the denominator.

The probability of an event based on its likelihood and the experimental probability of an event may be different. Probability-based likelihood is based on the structure of an experiment while experimental probability is based on the results of an experiment. The experimental results may differ from the likelihood of the event because they are real observations of outcomes, not likelihoods.

A spinner has five sections colored red, blue, green, black, and white A spinner has five sections colored red, blue, green, black, and white. In an experiment, red was spun 12 times, blue 3 times, green 20 times, black 5 times, and white 10 times. Find the experimental probability of spinning each color as a fraction in simplest form, a decimal, and a percent. Do you think the spinner is divided into equal sections? Explain.

A bag has tiles with pictures of different shapes A bag has tiles with pictures of different shapes. The table shows the results of drawing one tile at random from the bag, recording the shape, and then placing the tile back in the bag. Find the probability of each shape.

Typically, a soccer player gets an assist every other game Typically, a soccer player gets an assist every other game. Describe how you can use a standard deck of cards to model this situation. Then use a simulation to predict how many times in the next 12 games the soccer player will get an assist.

To play a game, you spin a spinner like the one shown To play a game, you spin a spinner like the one shown. You win if the arrow lands in one of the areas marked “WIN”. Lee played this game many times and recorded her results. She won 8 times and lost 40 times. Use Lee’s data to explain how to find the experimental probability of winning this game.

Mica and Joan are on the same softball team Mica and Joan are on the same softball team. Mica got 8 hits out of 48 times at bat, while Joan got 12 hits out of 40 times at bat. Who do you think is more likely to get a hit her next time at bat? Explain.

In tennis, Gabby serves an ace, a ball that can’t be returned, 4 out of the 10 times she serves. What is the experimental probability that Gabby will serve an ace in the first match of the next game? Make a prediction about how many aces Gabby will have for the next 40 serves. Justify your reasoning.

Talia tossed a penny many times. She got 40 heads and 60 tails Talia tossed a penny many times. She got 40 heads and 60 tails. She said the experimental probability of getting heads was 40 60 . Explain and correct her error.

Exit Ticket 2. When playing tennis, Dylan gets his first serve in play 75% of the time. Describe how you can use 12 index cards to model this situation. Then use a simulation to predict how many times in the next 20 serves Dylan will get his first serve in play. Explain thoroughly.