Do Now

In a phys ed class at LaGuardia, 13 students out of 50 have a cat as a pet.

If there are 2,813 students attending the school,

to the nearest 10, how many of them have cats as pets?

Do Now

In a phys ed class at LaGuardia, 13 students out of 50 have a cat as a pet.

If there are 2,813 students attending the school,

to the nearest 10, how many of them have cats as pets?

730

Do Now

In a phys ed class at LaGuardia, 13 students out of 50 have a cat as a pet.

If there are 2,813 students attending the school,

to the nearest 10, how many of them have cats as pets?

1350

= 0.26

(2813)(0.26) = 731 which rounds to 730

Puzzle # Title Page #

75 Modeling with Trig Functions

76 Trigonometric Identies

77 Probability

78 Empirical Probability

79 Independent & Dependent Events

Puzzle # 79

How do independent and dependent events compare with each other?

You toss a coin and roll a 4-sided die.

What is the probability you’ll get heads and a 3?

Think - 30 seconds

You toss a coin and roll a 4-sided die.

Explain to one member of your group what the probability is

that you’ll get heads and a 3?

Pair - 20 seconds

You toss a coin and roll a 4-sided die.

Share with your group what the probability is

that you’ll get heads and a 3?

Share - 20 seconds

How does the toss of the coin affect the die?

When the result of one activity has no influence

on the result of subsequent activities, they are independent events.

Flipping a coin has two possible outcomes: heads or tails

Rolling a 4-sided die has four possible outcomes: 1, 2, 3, or 4

H

T

1

2

3

41

2

3

4

Tree Diagram

H1 H2 H3 H4 T1 T2 T3 T4

P(H3) =18

If there are a lot of possible outcomes making a tree diagram

can be very time consuming.

Fortunately, there’s a faster way to figure it out.

P(A and B) = P(A) • P(B)

When two events are independent the product of both events happening

is the product of the probability of each event.

If the product of two events happening is their product,

the events are independent.

Let’s look at the problem from the Think-Pair-Share

P(H3) =18

P(H) =12

P(3) =14

Since P(H3) = P(H) • P(3), the events are independent

At Seaside Seafood, their salmon delivery comes 90% of the time,

40% of the customers order salmon, and there’s a 45% probability

that the salmon will be delivered and a customers will order it.

P(both) ≠ P(delivery) • P(order)

.45 ≠ .9 • .4

Therefore, the two events are not independent.

(Customers only order salmon if it’s been delivered.)

There are 10 marbles in a box; four red, three blue, two green,

and one yellow.

What’s the probability of picking two red and one blue?

What’s the probability of the first marble you pick

being red?

What’s the probability of the second marble you pick

being red?

410

39

What’s the probability of the third marble you pick

being blue?

38

P(RRG) = ( 410 ) ( 3

9 ) ( 38 ) =

36720

When the result of one activity influences the results of subsequent activities,

those are dependent events.

Determine the probability of all three marbles

being the same color.

P(3Red) = ( 410 ) ( 3

9 ) ( 28 ) =

24720

P(3Blue) = ( 310 ) ( 2

9 ) ( 18 ) =

6720

P(3Green) = 0, since there are fewer than 3 green marbles.

P(3Yellow) = 0, since there are fewer than 3 yellow marbles.

Determine the probability of all three marbles

being the same color.

P(3Red) = ( 410 ) ( 3

9 ) ( 28 ) =

24720

P(3Blue) = ( 310 ) ( 2

9 ) ( 18 ) =

6720

P(3All) =24720

+6

720=

30720

Exit Card # 79On a given school day,

the probability that Nick oversleeps is 48% and the probability he has a pop quiz is 25%. Assuming these two events are independent, what is the probability that Nick oversleeps

and has a pop quiz on the same day?

06_18_11

1) 73%

2) 36%

3) 23%

4) 12%

Exit Card # 79On a given school day,

the probability that Nick oversleeps is 48% and the probability he has a pop quiz is 25%. Assuming these two events are independent, what is the probability that Nick oversleeps

and has a pop quiz on the same day?

06_18_11

1) 73%

2) 36%

3) 23%

4) 12%

Exit Card # 79On a given school day,

the probability that Nick oversleeps is 48% and the probability he has a pop quiz is 25%. Assuming these two events are independent, what is the probability that Nick oversleeps

and has a pop quiz on the same day?

1) 73%

2) 36%

3) 23%

4) 12%

Since the two events are independent, 0.25 • 0.48 = 0.12