Warm-Up 4/30. Rigor: You will learn how to compute the theoretical and experimental probabilities and compute probabilities of compound events. Relevance:

Warm-Up 4/30

Rigor:You will learn how to compute the theoretical and experimental probabilities and compute

probabilities of compound events.

Relevance:You will be able to solve theoretical and

experimental probability problems and be able to find probabilities of compound events.

0-5 Adding Probabilities

Probability is a measure of the chance that a given event will occur.

A probability model is a mathematical model used to represent the outcomes of an experiment.

A uniform or simple probability model is used to describe an experiment for which the outcomes are equally likely or have the same probability of occurring.

The theoretical probability that an event will occur using the sample space of possible outcomes.

The experimental probability that an event will occur using outcomes obtained by actually performing trails of the experiment.

Key Concept: Theoretical ProbabilityIf each outcome is assumed to be equally likely, the theoretical probability P of an event E is given by

.

Experimental ProbabilityGiven the frequency of outcomes from a certain number of trials of an experiment, the experimental probability P of an event E is given by

.

Example 1: The graph shows the results of several trials of an experiment in which a single die is rolled.

a.What is the experimental probability of rolling a 6?

b. What is the theoretical probability of rolling a 6?

𝑃 (6)=Number of favorable outcomesNumber of possible outcomes

𝑃 (6)=Number of favorable trials

Number of trials

𝑃 (6)=1050

Total number of trials is 50.

¿15 This is 20%.

𝑃 (6)=16 This is 16.7%.

Your Turn:The graph shows the results of several trials of an experiment in which a spinner with eight equal sections of different colors is spun.

a.What is the experimental probability of spinning yellow?

b. What is the theoretical probability of spinning yellow?

Total number of trials is 80.

𝑃 (𝑌 )=1 480¿

740 This is 17.5%.

𝑃 (𝑌 )=18 This is 12.5%.

A simple event is an event that has a single outcome.

A compound event is an event which consists of two or more simple events.

Mutually exclusive events have no outcomes in common.

Key Concept: Addition Rule for Probability Mutually Exclusive Events If two events A and B are mutually exclusive, the probability, that A or B will occur is

.

Not Mutually Exclusive Events If two events A and B are not mutually exclusive, the probability, that A or B will occur is

.

Example 2a: Determine whether the events are mutually exclusive or not mutually exclusive. Then find the probability.

Keisha has a stack of 8 baseball cards, 5 basketball cards and 6 hockey cards. If she selects a card at random from the stack, what is the probability that it is a baseball card or a hockey card?

Events are mutually exclusive.

.

¿8

19 ¿1419

. Total number of cards is 19.

+619

Example 2b: Determine whether the events are mutually exclusive or not mutually exclusive. Then find the probability.

Suppose that of 1400 students, 550 take Spanish, 700 take biology, and 400 take both Spanish and biology. what is the probability that a student selected at random takes Spanish or biology? Events are not mutually exclusive.

𝑃 (S∨B )=𝑃 (S)+𝑃 (B )−𝑃 (S∧B)

𝑃 (S∨B )= 5501400

¿1728

DO NOT SIMPLIFY FRACTIONS UNLESS YOU WILL HAVE A COMMON DENOMINATIOR.

¿850

1400

+7001400−

4001400

Your Turn:Determine whether the events are mutually exclusive or not mutually exclusive. Then find the probability.

Nancy has a box of dog toys that contains 8 squeaky toys, 5 plush toys, and 2 bones. if she selects a toy at random from the box, what is the probability that it is a plush toy or a bone?

Events are mutually exclusive.

𝑃 (𝑃 𝑜𝑟 𝐵)=5

15¿

715

+215

AssignmentProb/Stats #2 WS, 1-10 All

Conics Project Sections 3 & 4 + 1 & 2 due today. YOU MUST HIGHLIGH CORRECTIONS USING A BLUE HIGHLIGHTER.

Senior Calculators returned by 5/7.All others Calculators returned by 5/14.