Adding Probabilites

0.5

Probability:

• the likelihood the event will occur. • must be a # between 0 and 1• Certain to occur: probability of 1• Cannot occur: probability of 0• Equally likely to occur or not occur:

probability of ½ (50% or .5)

(Theoretical) Probability

• When all outcomes are equally likely that an event will occur is:

• P(A) = number of outcomes in Atotal number of outcomes

• Simply called the probability of an event

Example 1: Find the probability.

A spinner has 8 equal-size sectorsnumbered from 1 to 8.

a) Spinning a 6b) Spinning an even numberc) Spinning a number greater than 5

Experimental Probability

• used when it is impossible or inconvenient to find the theoretical probability.

• used by performing an experiment, conducting a survey, or looking at the history of the event.

Example 2: Find the probability.Ninth graders must enroll in one math class. Theenrollments of ninth grade students during the previousyear are shown in the bar graph. Find prob. that a randomlychosen student from this year’s 9th grade class is in enrolled in

• a) Consumer Math• b) Algebra 1 or Intro to Algebra

87

36

69

51

0

20

40

60

80

100

Algebra 1 Consumer Math Geometry Intro to Algebra

Compound Events

• Union: when you consider ALL the outcomes for either of two events A and B. (A, B, A&B)

• Intersection: when you consider only the outcomes shared by both A and B. (A&B)

• Mutually Exclusive Events: if there is no intersection of A & B (Nothing in common)

IF A & B INTERSECT: P(A or B) = P(A) + P(B) – P(A&B)(Since P(A) and P(B) both include P(A &

B))

IF A & B ARE MUTUALLY EXCLUSIVE: P(A or B) = P(A) + P(B)

BA

BA

BA

UNION of A and B INTERSECTION of A and B INTERSECTION is empty

P(A or B) P(A and B) mutually exclusive events

Example 3

• One six-sided die is rolled.

• a) What is the probability of rolling a multiple of 3 or a 5?

• b) What is the probability of rolling a multiple of 3 or a multiple of 2?

Example 4

In a poll of high school juniors, 6 out of 15 took a French class and 11 out of 15 took a math class. Fourteen out of 15 took French or math. What is the probability that a student took both French and Math?

Example 5

You have an equally likely chance of rolling any value on each of two dice. Find the probability of rolling….• a) a sum of either 3 or 11

• b) doubles or a sum or 8

• c) a nine on exactly one die

Warm up

In a survey of 200 pet owners, 103 owned dogs, 88 owned cats, 25 owned birds, and 18 owned reptiles.

a) None of the respondents owned both a cat and a bird. What is the probability that they owned a cat or a bird?

b) Of the respondents, 119 owned a dog or a reptile. What is the

probability that they owned a dog and a reptile?

Example 6: Find the probability.Five cards are drawn from a standard 52-card deck.

a) Choosing exactly all red cardsb) Choosing exactly 2 even numbered

card and 3 face cardsc) Choosing exactly three fives

Probability involves Combinations!!

Example 7

• Seven marbles are chosen at random from a jar containing 15 green marbles and 11 white marbles. Find the probability of the following:

• A) choosing 4 green marbles and 3 white marbles

• B) choosing exactly one white marble