Probability Notes

•Probability: How likely it is that a particular event will occur.

•When the outcomes are equally likely, the probability of an event is written as a ratio:

P= Number of favorable outcomes

Total number of outcomesTheoretical Probability = Probability that is determined on the basis of reasoning, not through experimentation. This is what you think WILL happen based on the situation.

Experimental Probability = A probability calculated from the results of an experiment. This is what actually happens when you conduct the experiment.

•If the event is impossible, its probability is O.Ex: The probability of drawing an 11 from cards numbered 1 to 10 is impossible.

•If an event is unlikely, equally likely, or likely, its probability is between 0 and 1. This can be written as a fraction, decimal, ratio, or percent.Ex: The probability that you will draw a 2 or a 4 from cards numbered 1 to 10 is likely.

•If an event is certain, its probability is 1. Ex: The probability that you will draw a card from 1 to 10 from a set of cards numbered 1 to 10 is certain.

•Find the probability of rolling a 5 on a die.

•Find the probability of rolling an even number on a die.

•Find the probability of rolling a seven on a die.

•Find the probability of rolling an even or odd number on a die.

Theoretical Probabilities Investigation 4 – How Likely Is It?

Follow Up to Problem 4.1o The probabilities you computed in part B are called experimental

probabilities because you found them by experimenting. o The fractions you found in part D are called theoretical probabilities

because you analyze the possible outcomes rather than actually experimenting.

If all the outcomes of an action are equally likely, then the theoretical probability of an event is done with this formula:

number of favorable outcomes number of possible outcomes

1. Compare the exp. prob. and theor. prob. you found – are they close to one another? Should they be? Why? Why not?

2. When you drew a block did each block have an equally likely chance of being chosen? Explain.

3. When you drew a block did each color have an equally likely chance of being chosen? Explain.

4. In the game show contestants select blocks randomly from the bucket. What do you think randomly means?

Theoretical Probabilities Investigation 4 – How Likely Is It?

Problem 4.2 Drawing More Blocks

Your teacher put eight blocks into a bucket. All blocks are the same size. Three are yellow, four are red, and one is blue.

1. Use your sheet for problem 4.2 to answer the questions.

Theoretical Probabilities Investigation 4 – How Likely Is It?

Problem 4.3 Winning the Bonus Prize

All the winners from the Gee Whiz Everyone Wins game show get an opportunity to compete for a bonus prize. Each winner draws one block from each of two bags, both of

which contain one red, one yellow, and one blue block. The contestant must predict which color she or he will draw

from each of the two bags. IF the prediction is correct the contestant wins a $10,000 bonus prize!

Use this information to solve problem 4.3.

Follow Up Question:

What if you are on the show and you’ve already won a mountain bike, a CD player, a vacation to Hawaii, and a one

year supply of Glimmer toothpaste. You lost the bonus round, but the host makes an offer: you can draw from the

two bags again, but this tme you do not predict the color. If the two colors match you will win $5000. If they do not

match you must return the prizes you’ve won. Would you accept this offer? Why or why not?