7/20 100 people were surveyed for their favorite fast-food restaurant. 1. What is the probability...

7/20

100 people were surveyed for their favorite fast-food restaurant.

1. What is the probability that a person likes Wendy’s?

2. What is the probability that a person is male who likes Burger King?

3. What is the probability that a person is likes McDonald’s or Burger King?

3/20

McDonald’s Burger King Wendy’s

Male 20 15 10

Female 20 10 25

13/20

Probabilities of Compound Events

UNIT QUESTION: How do you use probability to make plans and predict for the future?Standard: MM1D1-3

Today’s Question:When do I add or multiply when solving compound probabilities?Standard: MM1D2.a,b.

A compound event combines two or more events, using the word and or the word or.

If two or more events cannot occur at the same time they are termed mutually exclusive (disjoint).

They have no common outcomes.

Overlapping events have at least one common outcome.

Two events are independent if the occurrence of one event has no effect on the other

Two events are dependent if the occurrence of one event affects the outcome of the other

Lesson 6.4 p. 351

The probability is found by summing the individual probabilities of the events:

P(A or B) = P(A) + P(B)

A Venn diagram is used to show mutually exclusive events.

Mutually Exclusive Events

Example 1:

Find the probability that a girl’s favorite department store is Macy’s or Nordstrom.

Find the probability that a girl’s favorite store is not JC Penney.

Mutually Exclusive Events

Macy’s 0.25

Saks 0.20

Nordstrom 0.20

JC Penney 0.10

Bloomingdale’s 0.25

0.45

0.90

Example 2:

When rolling two dice, what is probability that your sum will be 4 or 5?

Mutually Exclusive Events

7/36

Example 3:

What is the probability of picking a queen or an ace from a deck of cards

Mutually Exclusive Events

2/13

Probability that overlapping events A and B or both will occur expressed as:

P(M or E) = P(M) + P(E) - P(ME)

Overlapping Events

Example 1:

Find the probability of picking a king or a club in a deck of cards.

Overlapping Events

4/13

Example 2:

Find the probability of picking a female or a person from Tennessee out of the 31 committee members.

Overlapping Events

Fem Male

TN 8 4

AL 6 3

GA 7 3

21 12 8 25

31 31 31 31

Example 3:

When rolling 2 dice, what is the probability of getting an even sum or a number greater than 10?

Overlapping Events

18 3 1 20

36 36 36 36

Independent Events

• Two events A and B, are independent if A occurs & does not affect the probability of B occurring.

• Examples- Landing on heads from two different coins, rolling a 4 on a die, then rolling a 3 on a second roll of the die.

• Probability of A and B occurring:

P(A and B) = P(A) ∙ P(B)

Experiment 1

• A jar contains three red, five green, two blue and six yellow marbles. A marble is chosen at random from the jar. After replacing it, a second marble is chosen. What is the probability of choosing a green and a yellow marble?

P (P (greengreen) = 5/16) = 5/16 P (P (yellowyellow) = 6/16) = 6/16 P (P (greengreen and and yellowyellow) = P (green) ) = P (green) ∙ P (yellow) P (yellow)

= 15 / 128= 15 / 128

Dependent Events

• Two events A and B, are dependent if A occurs & affects the probability of B occurring.

• Examples- Picking a blue marble and then picking another blue marble if I don’t replace the first one.

• Probability of A and B occurring:

P(A and B)=P(A) ∙ P(B given A)

Experiment 2

• A random sample of parts coming off a machine is done by an inspector. He found that 5 out of 100 parts are bad on average. If he were to do a new sample, what is the probability that he picks a bad part and then picks another bad part if he doesn’t replace the first?

P (bad) = 5/100P (bad) = 5/100 P (bad given bad) = 4/99P (bad given bad) = 4/99 P (bad and then bad) = 1/495P (bad and then bad) = 1/495

Experiment 3

• A jar contains three red, five green, two blue and six yellow marbles. A marble is chosen at random from the jar. A second marble is chosen. What is the probability of choosing a green and a yellow marble if the first marble is not replaced?

P (P (greengreen) = 5/16) = 5/16 P (P (yellowyellow) = 6/15) = 6/15 P (P (greengreen and and yellowyellow) = P (green) ) = P (green) ∙ P (yellow) P (yellow)

= 30 / 240 = = 30 / 240 = 1/81/8

Experiment 4

• A jar contains three red, five green, two blue and six yellow marbles. A marble is chosen at random from the jar. A second marble is chosen. What is the probability of choosing a green marble both times if the first marble is not replaced?

P (P (greengreen) = 5/16) = 5/16 P (P (greengreen) = 4/15) = 4/15 P (P (greengreen and and greengreen) = P (green) ) = P (green) ∙ P (green) P (green)

= 20 / 240 = = 20 / 240 = 1/121/12

P(A or B) = P(A) + P(B) P(A or B) = P(A) + P(B) - P(overlap)

P(A and B) = P(A) ∙ P(B) P(A and B) = P(A) ∙ P(B given A)

-Drawing a king or a queen

-Selecting a male or a female

-Selecting a blue or a red marble

-Drawing a king or a diamond

-rolling an even sum or a sum greater than 10 on two dice

-Selecting a female from Georgia or a female from Atlanta

WITH REPLACEMNT:

-Drawing a king and a queen

-Selecting a male and a female

-Selecting a blue and a red marble

WITHOUT REPLACEMENT:

-Drawing a king and a queen

-Selecting a male and a female

-Selecting a blue and a red marble

Classwork

• Get your WORKBOOK and do p. 369, #1-11 all

Homework

Pg. 353 1-8 all