Review ofProbability and Statistics

Algebra I

Chapter 4.3

Math Warm-Up

• Write each decimal as a fraction and percent.

• 3 / 4• 7/10• 2/9• 125/300

.75 or 75%

.70 or 70%

.222 or 22.2%

5/12=0.417 or 41.7%

Probability answers the question:

How likely will the event occur?

Probability

• Can be measured from 0 – 100%

• Most often is measured in fractions.

Experimental vs. Theoretical Probability

Experiments

• Are done many times

• Can sometimes have unexpected results

• Sometimes work the way you expect them to.

• Related to science and math

Theory

• Expectations

• Potential results

Experimental Probability

• Shake dice and count how many of each number

• Spin a spinner and count how many times it falls on red, blue, or green

• Flip a coin and record the results.

Theoretical Probability

• Use the number of possible outcomes divided by the total number of outcomes.

• Count

• Predict

How may possible outcomes?

• How many times could an even

number be rolled?

3 out of 6

3 out of 6

• As a fraction:

• One chance in every two is the theoretical probability of rolling an even number.

3

6 1

2

P (4)=

• How many fours on one cube?

• … out of how many numbers on a rolling cube?

• 1/6

Sample set

• Two Coins• H, H• H, T• T, H• T, T

Sample setThree Coins• H, H, H• H, H, T• H, T, T• H, T, H• T, H, H• T, H, T• T. T. H• T, T. T

P (1h and 1t) =?

• Matching outcomes (h,t) (t,h)

• Two chances in four

• 1 chance in every two.

• 50 % = ½

Sample SetTwo Dice

( 1, 1); ( 1, 2); ( 1, 3); ( 1, 4); ( 1, 5); ( 1, 6)

( 2, 1); ( 2, 2); ( 2, 3); ( 2, 4); ( 2, 5); ( 2, 6)

( 3, 1); ( 3, 2); ( 3, 3); ( 3, 4); ( 3, 5); ( 3, 6)

( 4, 1); ( 4, 2); ( 4, 3); ( 4, 4); ( 4, 5); ( 4, 6)

( 5, 1); ( 5, 2); ( 5, 3); ( 5, 4); ( 5, 5); ( 5, 6)

( 6, 1); ( 6, 2); ( 6, 3); ( 6, 4); ( 6, 5); ( 6, 6)

( 1, 1); ( 1, 2); ( 1, 3); ( 1, 4); ( 1, 5); ( 1, 6)( 2, 1); ( 2, 2); ( 2, 3); ( 2, 4); ( 2, 5); ( 2, 6)( 3, 1); ( 3, 2); ( 3, 3); ( 3, 4); ( 3, 5); ( 3, 6)( 4, 1); ( 4, 2); ( 4, 3); ( 4, 4); ( 4, 5); ( 4, 6)( 5, 1); ( 5, 2); ( 5, 3); ( 5, 4); ( 5, 5); ( 5, 6)( 6, 1); ( 6, 2); ( 6, 3); ( 6, 4); ( 6, 5); ( 6, 6)

• What is the probability of shaking a one?• What is the probability of shaking doubles?• p (even, even) =• p (3, odd) =• p (odd, odd) =• p (even, even) =• p (total >5) =• p (total < 7) =

Use two dice

6 red buttons and 3 blue buttons

9 buttons are placed into a bag

What is the chance ofblindly drawing a red button?

Six favorable outcomes out of nine buttons

6 2

9 3

266.67%

3

From the bag

• What is the chance of pulling out a blue button?

• 3 out of 9

3 1

9 3 33%

When figuring theoretical probability

• Find the number of favorable outcomes

• Find the number of possible outcomes

• Make a fraction.

• Put the fraction in lowest terms

• Divide for the decimal

• Move 2 places for %favorable

possible

Assignment

Pg 183-184:

12-17; 18-27