An outcome is a possible result An event is a specific outcome Random means all outcomes are equally likely to occur or happen. random = fair A favorable.

7.8 SIMPLE PROBABILITY

An outcome is a possible result

An event is a specific outcome

Random means all outcomes are equally likely to occur or happen.

random = fair

A favorable event is the outcome you’re looking for

The probability that an event will happen is a number between 0 and 1:

A probability of 0 means the event will definitely NOT happen.

A probability of 1 means the event definitely WILL happen.

All other probabilities are between 0 and 1

0Impossibl

e

1Definite

50-50 chance

Probability

The probability that an event will happen can be also described as a percent.

0Impossibl

e

100%Definite50%

2

1

Probability is the chance that some event will happen.

It can be written as a ratio.

# of favorable outcomes (what you want)total # of possible outcomes

There are 2 types of probabilities:1) Theoretical

2) Experimental

Theoretical probability is calculated. # of favorable outcomes # of possible outcomesExperimental probability is based on actual results (something you did and counted).

Now turn to page 383 and try Guided Practice problems 1 and 2

Guided Practice problem 1

You roll a number cube (dice) 100 times. Your results are given in the table below.

Number

1 2 3 4 5 6

Rolls 17 15 20 16 14 18

What is the experimental probability of rolling a number greater than 3?

Remember, experimental probability is based on something that you actually did! So use the numbers in the chart.

Probability = number of favorable outcomes number of total outcomes

P = 16 + 14 + 18________ 17 + 15 + 20 + 16 + 14 + 18

P =

Guided Practice problem 1 continued

You roll a number cube (dice) 100 times. Your results are given in the table below.

Number

1 2 3 4 5 6

Rolls 17 15 20 16 14 18

What is the theoretical probability of rolling a number greater than 3?

Remember, theoretical probability is based the possible outcomes.

Probability = number of favorable outcomes number of total outcomes

P =

Guided Practice problem 1 continued

You roll a number cube (dice) 100 times. Your results are given in the table below.

Number

1 2 3 4 5 6

Rolls 17 15 20 16 14 18

So the experimental probability of rolling a number greater than 3 was 48% based on the experiment that was done.

Theoretical probability or calculated probability was 50%.

The experimental probability becomes more accurate or closer to the theoretical probability when there are more trials.

Guided Practice problem 2

Use the information in Example 3. About how many buttons would you expect to be defective in a shipment of 25,000 buttons?

A company manufactures buttons. A quality control inspector finds 2 defective buttons in a batch of 300 buttons. About how many

buttons would you expect to be defective in a shipment of 25,000 buttons?

Use cross products to find the answer.

2𝑑𝑒𝑓𝑒𝑐𝑡𝑖𝑣𝑒300𝑏𝑢𝑡𝑡𝑜𝑛𝑠

=𝑥𝑑𝑒𝑓𝑒𝑐𝑡𝑖𝑣𝑒25,000𝑏𝑢𝑡𝑡𝑜𝑛𝑠

300x = 50,000 divide both sides by 300

x = 166

About 167 buttons

Independent Events – events that do not effect each other

To calculate the probability of 2 independent events: Find the probability of each one, then multiply

Ex. What is the probability of rolling a 1 and then rolling a 2 on a standard die.

P(1) = P(2) = P(1 then 2) = 6

1

6

136

1

Probability of Compound Events

Let’s try some:Suppose you roll a red die and a blue die. What is the probability that you will roll a 5 on the red and a 1 or 2 on the blue.

The probability of rolling a 5 is16

The probability of rolling a 1 or a 2 is

To find the probability of BOTH, multiply them:

16∗26=236

𝑜𝑟118

The probability that you will roll a 5 on the red and a 1 or 2 on the blue is r 5.6%

There is a bag of marbles. There are 4 white, 3 black, 8 purple, 2 red, and 8 green.Find the probability of choosing a purple, then a red

after replacing the 1st marble.The probability of choosing a purple marble first is since there are 8 purple marbles out of 25 total marbles. Since I am replacing the purple one after I picked it, the probability of picking a red marble next is because there are 2 red marbles out of 25 total.

To find the probability of picking a purple and then a red, you multiply the two probabilities together.

* = or about 2.6%

There is a bag of marbles. There are 4 white, 3 black, 8 purple, 2 red, and 8 green.Find the probability of choosing a purple, then a red

without replacing the 1st marble.The probability of choosing a purple marble first is since there are 8 purple marbles out of 25 total marbles. Since I am NOT replacing the purple one after I picked it, the probability of picking a red marble next is because there are 2 red marbles out of 24 total.

To find the probability of picking a purple and then a red, you multiply the two probabilities together.

* = or about 2.7%

If you are feeling confident about simple probability,

you can get a head start on the classwork.

Pages 383 – 3851-23

Compound probability will NOT be on the test! If you don’t get

it, don’t worry…we will talk about it in class.