Unit: Probability 12-2: Conditional Probability

10
Essential Question: What makes conditional probability different from normal probability?

description

Essential Question: What makes conditional probability different from normal probability?. Unit: Probability 12-2: Conditional Probability. - PowerPoint PPT Presentation

Transcript of Unit: Probability 12-2: Conditional Probability

Page 1: Unit: Probability 12-2: Conditional Probability

Essential Question: What makes conditional probability different from normal probability?

Page 2: Unit: Probability 12-2: Conditional Probability

A conditional probability contains a condition that may limit the sample space for the event. We can write a conditional probability event using the notation P(B | A), which means “the probability of event B, given event A”.

Order matters when calculating conditional probability.

We can calculate conditional probability from a table (next slide)

Page 3: Unit: Probability 12-2: Conditional Probability

The table below shows the results of a class survey if students did a household chore last night. Find P(did a chore | male)

The second condition limits the sample space to only males (15 total). Of those 15, 7 did a chore, so P(did a chore | male) = 7/15

Use the table above to find P(female | did a chore)

Yes

No

Male 7 8

Female

7 6

7/14 = 1/2

Page 4: Unit: Probability 12-2: Conditional Probability

YOUR TURN The table below shows recycling data

for a recent year. Find the probability that a sample of recycled waste was paper.

Find P(paper | recycled)

36.7/68 .54

Material

Recycled

Not Recycled

Paper 36.7 45.1

Metal 6.3 11.9

Glass 2.4 10.1

Plastic 1.4 24.0

Other 21.2 70.1

Page 5: Unit: Probability 12-2: Conditional Probability

You can use a formula to find conditional probability

P(B | A) = P(A and B)P(A)

Example: 80% of an airline’s flights depart on schedule. 72% of its flights depart and arrive on schedule. Find the probability that a flight that departs on time also arrives on time.

.72/.80 = 0.9

Page 6: Unit: Probability 12-2: Conditional Probability

YOUR TURN P(B | A) = P(A and B)

P(A) Researchers asked people who exercise

regularly whether they jog or walk. 58% of the respondents were male. 20% of all respondents were males who said they jog. Find the probability that a male respondent jogs.

.20/.58 = 0.34 (about 34%)

Page 7: Unit: Probability 12-2: Conditional Probability

You can use a tree diagram to solve problems involving conditional probabilities.

A student in Buffalo, NY made the following observations: Of all snowfalls, 5% are heavy (at least 6 in) After a heavy snowfall, schools are closed 67%

of the time After a light (less than 6 in) snowfall, schools

are closed 3% of the time. Find the probability that the snowfall is light

and the schools are open (next slide)

Page 8: Unit: Probability 12-2: Conditional Probability

5% are heavy snowfall After heavy, 67% chance school closed After light, 3% chance school closed Find P(light snow and schools open)

0.05

0.95

Heavy

Light

0.67

0.33

0.03

0.97

Closed

Open

Closed

Open

0.95 0.97 = 0.92

Page 9: Unit: Probability 12-2: Conditional Probability

YOUR TURN Find P(schools open and heavy snow)

0.05

0.95

Heavy

Light

0.67

0.33

0.03

0.97

Closed

Open

Closed

Open

0.05 0.33 = 0.0165

Page 10: Unit: Probability 12-2: Conditional Probability

ASSIGNMENT Page 656 – 657

Problems 1 – 12 (all)