1. Determining the theoretical probability of an event
Lesson 14
Determining the theoretical probability of an event

2. Probability terms
Sample space is the set of all possible outcomes of an event- tossing a fair coin has 2 equally likely outcomes, so has a sample space of 2
Simple event is an event having only one outcome- rolling a 5 on a dice
Theoretical probability of an outcome is found by finding the ratio of favorable outcomes to all possible outcomes
favorable outcomes
all possible outcomes

3. Identifying sample spaces
A number cube labeled 1-6 is rolled.
List the outcomes for each event:
1. a number less then or equal to 3
2. an odd number
3. an even number
4. a multiple of 3
5. a prime number

4. Complement of an event
The set of all outcomes that are not in a given event.
If heads is the desired outcome when tossing a coin, then tails is the complement
The sum of an event and its complement = 1
P (event) + P (not event) = 1

5. Probability can be expressed as fractions, decimals, or percents
hint !!!
Probability can be expressed as fractions, decimals, or percents

6. Calculating theoretical probability
Suppose there are 4 green, 3 blue and 3 red marbles in a bag. Give each answer as a decimal and percent,
1. what is the probability of choosing a red marble? P (red)= 3/10,, .3, 30%
2. what is the probability of choosing a marble that is not red?
P (not red)= 7/10, .7 , 70% OR
P (not read) = 1-P(red)= 1-.3= .7

7. Chance Chance is the likelihood of an event occurring.
Calculating chance-
Ex: in a bucket there are 10 balls numbered as follows: 1,1,2,3,4,4,4,5,6,6.
A single ball is randomly drawn from the bucket.
What is the probability of drawing a ball with a number greater than 4?
Is there a greater chance of drawing a number greater than 4 or a 1?

8. solution
P (greater than 4) = 3/10 or .3
P (1) = 2/10 = .2
.3 > .2 so there is a greater chance of drawing a number greater than 4

9. Lab 1 generating random numbers
A set of random integers has no pattern. We can generate random numbers by rolling a dice or drawing numbers out of a hat. We can also generate random integers by using a graphing calculator.

10. Generate 3 random numbers between 1 and 12
1. Press MATH and then the right arrow key 3 times until you get to PRB
2. Go down to 5:randInt(
3. press enter
4. identify the range of values you want- 1 through 12 by pressing 1,12)
5. press enter to get the 1st integer
6. press enter 2 more times to get 2 more random integers.

11. Lab practice
Jared lost the dice to his favorite board game, but he does have a graphing calculator. According to the rules, the player should throw 2 dice and move the total number of spaces shown on the top of the 2 dice.
1. What range of numbers does a single dice generate? What should he enter in his calculator to simulate the dice?
2. How can he simulate rolling 2 dice?
3.simulate Jared taking 3 turns. What number of spaces will he move in each turn? What is the total number of spaces moved?

12. Investigation 1 determining the probability of an event
Probability is the measure of how likely a given event will occur.
An outcome is a possible result of a probability experiment.
An event is an outcome or set of outcomes in a probability experiment

13. Range of probability Impossible as likely as not certain
unlikely likely
______________________________________________________
0% % %

14. Describe each event below as impossible, unlikely, as likely as not, likely, or certain.
1. Jake rolls a number less then 7 on a dice.
Certain
2. February will have 30 days
Impossible
3. A tossed coin will land on heads
As likely as not
4. Shayla will correctly guess a number between 1 and 100
unlikely

15. Experimental probability
Experimental probability is the measure of how likely a given event will occur based on repeated trials.
Experimental probability= number of times an event occurs
number of trials

16. follow directions to complete investigation 1 activity

17. Experimental probability in sports
A player's batting average is the probability of a player getting a hit based on his previous at bats. It is usually expressed as a decimal to the thousandths place.
If a player gets 8 hits in 25 at bats, what is the probability that he will get a hit on his next at bat?
8/25= .320

18. Random events
A random event is an event whose outcome cannot be predicted.
Ex. Drawing a card labeled 8 from a bin of cards, each labeled with a number from 1 to 100, is a random event.
We could conduct an experiment and find the experimental probability, but sometimes it is not practical to do this.
So sometimes we perform a simulation of a random event using models such as dice, spinners, coins, or random number generators.

19. activity
Saxon O's cereal is having a contest. Each box of cereal contains a prize piece and claims that 1 in 8 pieces is a winner. Conduct a simulation to determine the experimental probability of winning a prize piece within 50 boxes of cereal.
1. use the digits 1 through 8
2. generate 50 random numbers
3. what is the probability of winning a prize, according to your simulation.
4. how does your answer compare to the company's claim?