Warm upWarm upDecide if the following represent permutations or Decide if the following represent permutations or

combinations. Then calculate the desired results.combinations. Then calculate the desired results.

1.1. How many different four digit numbers can be created from the numbers How many different four digit numbers can be created from the numbers

six, two, three, eight, and five?six, two, three, eight, and five?

2.2. There are 22 students in a dance class here at Perry. How many There are 22 students in a dance class here at Perry. How many

different ways can 3 dancers be chosen for a routine?different ways can 3 dancers be chosen for a routine?

5 45! 120

(5 4)!P

22 322! 1540

3!(22 3)!C

Experimental Probability Experimental Probability vs. Theoretical vs. Theoretical

ProbabilityProbability

Lesson 14.9Lesson 14.9

What do you know about probability?What do you know about probability?

►Probability is a number from 0 to 1 Probability is a number from 0 to 1 that tells you how likely something is that tells you how likely something is to happen.to happen.

►Probability can have two approaches Probability can have two approaches -experimental probability-experimental probability

-theoretical probability-theoretical probability

Experimental vs.TheoreticalExperimental vs.TheoreticalExperimental probability:Experimental probability:P(event) = P(event) = number of times event occursnumber of times event occurs total number of trialstotal number of trials

Theoretical probability:Theoretical probability:P(E) = P(E) = number of favorable outcomesnumber of favorable outcomes

total number of possible outcomestotal number of possible outcomes

How can you tell which is experimental and How can you tell which is experimental and which is theoretical probability?which is theoretical probability?

Experimental:Experimental:You tossed a coin 10 You tossed a coin 10

times and recorded times and recorded a head 3 times, a a head 3 times, a tail 7 timestail 7 times

P(head)= 3/10P(head)= 3/10P(tail) = 7/10P(tail) = 7/10

Theoretical:Theoretical:Toss a coin and Toss a coin and

getting a head or a getting a head or a tail is 1/2.tail is 1/2.

P(head) = 1/2P(head) = 1/2P(tail) = 1/2P(tail) = 1/2

Experimental probabilityExperimental probability

Experimental probability is found by Experimental probability is found by repeating an repeating an experimentexperiment and and observing the observing the outcomesoutcomes..

P(head)= 3/10A head shows up 3 times out of 10 trials

P(tail) = 7/10A tail shows up 7 times out of 10 trials

Theoretical probabilityTheoretical probabilityP(head) = 1/2P(head) = 1/2P(tail) = 1/2P(tail) = 1/2Since there are only Since there are only

two outcomes, two outcomes, you have 50/50 you have 50/50 chance to get a chance to get a head or a tail. head or a tail.

HEADS

TAILS

Compare experimental Compare experimental and theoretical and theoretical

probabilityprobabilityBoth probabilities are ratios that Both probabilities are ratios that compare the number of favorable compare the number of favorable outcomes to the total number of outcomes to the total number of possible outcomespossible outcomes

P(head)= 3/10P(tail) = 7/10

P(head) = 1/2P(tail) = 1/2

Identifying the Type of ProbabilityIdentifying the Type of Probability

► A bag contains A bag contains three red marbles three red marbles and three blue and three blue marbles.marbles.

P(red) = 3/6 =1/2P(red) = 3/6 =1/2 Theoretical Theoretical (The result is based on (The result is based on

the possible the possible outcomes)outcomes)

Identifying the Type of ProbabilityIdentifying the Type of Probability

Trial Red Blue

1 1

2 1

3 1

4 1

5 1

6 1

Total 2 4

Exp. Prob. 1/3 2/3

► You draw a marble out of You draw a marble out of the bag, record the color, the bag, record the color, and replace the marble. and replace the marble. After 6 draws, you record 2 After 6 draws, you record 2 red marblesred marbles

P(red)= 2/6 = 1/3P(red)= 2/6 = 1/3

ExperimentalExperimental((The result is found by The result is found by

repeating an experiment.)repeating an experiment.)

Lesson ReviewLesson Review►Probability tells you the likelihood that Probability tells you the likelihood that

something will happensomething will happen►There are two types of probabilityThere are two types of probability►Theoretical--- theoretical measurement Theoretical--- theoretical measurement

and can be found without experimentand can be found without experiment►Experimental--- measurement of a Experimental--- measurement of a

actual experiment and can be found by actual experiment and can be found by recording experiment outcomesrecording experiment outcomes

Class work (optional)Class work (optional)

Have students break into groups of two or three. Have students break into groups of two or three. Calculate the theoretical probability of flipping a Calculate the theoretical probability of flipping a coin or rolling a dice. Have them take out a penny coin or rolling a dice. Have them take out a penny or hand out a dice to each group and have them or hand out a dice to each group and have them do 10 trials and compare to theoretical probability. do 10 trials and compare to theoretical probability. Do 10 more trials and compare after 20 trials. If Do 10 more trials and compare after 20 trials. If time permits have them do 10 more trials and see time permits have them do 10 more trials and see how the probability compares each time.how the probability compares each time.