Consecutive Trials (multiple events)• Consecutive trials are when a situation occurs

multiple times– I draw two, three, four or more cards.– I throw the die two, three, four, or more times– I draw two, three, four, or more marbles from a bag

• Independent Events– Events that are considered separately each on different

consecutive trials.

• Dependent Events– Events that are considered together on different

consecutive trials

Wednesday, August 26, 2015DO NOW

1.In your own words, describe what the word independent means

2.In your own words, describe what the word dependent means

3.Give 2 examples of each

Probability of Independent & Dependent Events

Vocabulary:•Dependent Events

– The occurrence of one event influences the other event.•Independent Events

– The occurrence of one event does not depend on the occurrence of the other event.

• Conditional Probability– The probability that B will occur given that A has

occurred.

Probability of Independent Events

• If A and B are independent events, then the probability that both A and B occur is:

= X

Written: P(A and B) = P(A) x P(B)

A B P(A) P(B)

SAT Test Practice

• For a fundraiser, a class sells 150 raffle tickets for a mall gift certificate and 200 raffle tickets for a book of movie passes. You buy 5 raffle tickets for each prize. What is the probability that you win both prizes?

1 1 1 1) ) ) )

6000 1200 350 70 a b c d

In the previous example, what is the probability that you win the mall gift certificate but not the booklet of movie passes?

Find Probability of 3 Independent Events

• In BMX meet, each heat consists of 8 competitors who are randomly assigned lanes from 1 to 8. What is the probability that a racer will draw lane 8 in the 3 heats in which the racer participates?

•A game spinner is divided into ten equal regions numbered 1 to 10. What is the probability that 3 consecutive spins result in perfect squares?

STOP & Practice

Dependent Events

• If A and B are dependent events, then the probability that both A and B occur is:

P(B|A) is read “the probability that B occurs given that A has occurred”

and P A B P A P B A

Comparing independent and dependent events

You randomly select two cards from a standard deck of 52 cards. What is the probability that the first card is not a heart and the second is a heart if

a) you replace the first card before selecting the second

b) you do not replace the first card?

& P A B P A P B A 39 13 13

52 51 68

& P A B P A P B39 13 3

52 52 16

Independent

Dependent

Find probability of 3 dependent events

• Ann , Sue, then Jane go to the same store at different times to buy costumes for a costume party. There are 15 different types of costumes at the store, and the store has at least 3 duplicates of each costume. What is the probability that they each choose different costumes.

A – Ann chooses a costumeB – Sue chooses a costume different than Ann’sC – Jane chooses a costume different than Ann’s and Sue’s

P(A & B & C) = P(A) x P(B|A) x P(C|A & B)

15 14 13 182

15 15 15 225

Thursday, August 27, 2015DO NOW

Conditional Probability

• Conditional probability is the probability of something happening given a limiting condition.– What is the probability of drawing a queen of spades given the card

is black?P(queen of spades|black)

– What is the probability of rolling a 12 sided die and getting a 4 given the number is even?P(4|even)

1

26 /A

P A BB

1

6 /A

P A BB

Find a conditional probabilityThe table shows the numbers of tropical cyclones that formed during

the hurricane seasons from1988 to 2004. Use the table to estimate a) the probability that a future tropical cyclone is a hurricane and b) the probability that a future tropical cyclone in the Northern Hemisphere is a hurricane.

Type of Cyclone Northern Hemisphere

Southern Hemisphere

Tropical depression 199 18

Tropical storm 398 200

Hurricane 545 215

Use the information in the Cyclone table to find a)The probability that a future tropical cyclone is a tropical storm.

b) The probability that a future tropical cyclone in the Southern Hemisphere is a tropical storm.

Find the probability of drawing the given cards from a standard deck a) with replacement and b) without replacementA spade, then a club A jack, then another jack

Type of Cyclone Northern Hemisphere

Southern Hemisphere

Tropical depression 199 18

Tropical storm 398 200

Hurricane 545 215

Whats a Deck of Cards look like?

• contingency tables show frequencies produced by cross-classifying observations

• e.g., pottery described simultaneously according to vessel form & surface decoration

polished burnished matte

bowl 47 28 3

jar 30 42 8

olla 6 45 25

PROBLEM: 1.Give the total number of outcomes of choosing a hamburger, hot dog, or chicken and potato salad, coleslaw, or beans. Use a tree diagram.

• Answer:

Hamburger

Hot dog

chicken

potato salad

potato salad

potato salad

beans

beans

beans

coleslaw

coleslaw

coleslaw

AFM/Math 3 Material:

https://www.mathsisfun.com/data/probability-events-conditional.html

Lets draw a picture…

Safety

Using observations made of drivers arriving at a certain high school, a study reports that 69% of adults wear seat belts while driving. A high school student also in the car wears a seat belt 66% of the time when the adult wears a seat belt, and 26% of the time when the adult does not wear one. What is the probability that a high school student wears a seat belt?

A – Adult is wearing a seat belt

B – Student wears a seat belt

& & | or c c cP A B A B P A P B A P A P B A

0.69 0.66 0.31 0.26 0.4554 0.0806 0.536

A high school basketball team leads at halftime 60% of the games in a season. The team wins 80% of the time when they have the halftime lead, but only 10% of the time when they do not. What is the probability that the team wins a particular game during the season?