Lesson 6 Striving for Independence Practice Understanding

Ready

Solve each quadratic equation.

1.

$m^{2} + 15 m + 56 = 0$

2.

$5 x^{2} - 3 x + 7 = 0$

3.

$x^{2} - 10 x + 21 = 0$

4.

$6 x^{2} + 7 x - 5 = 0$

Set

5.

A group of students was observed to determine whether or not they wear glasses and whether or not they wear a hooded sweatshirt. The data is shown in the table. Use the data to respond to the problems.

	Glasses	No Glasses	Total
Hoodie	$20$	$10$	$30$
No Hoodie	$10$	$20$	$30$
Total	$30$	$30$	$60$

a.

How many students were observed?

b.

$P (Glasses) =$

c.

$P (Hoodie) =$

d.

$P (Glasses and Hoodie) =$

e.

$P (Glasses | Hoodie) =$

f.

For this sample, are wearing glasses and wearing a hoodie independent events? Why or why not?

6.

The principal at a school checked student class schedules to see if they were enrolled in world languages or music classes. She compiled the data in the table below. Use the data to find the probabilities and answer the following problems.

	Music	No Music	Total
Language	$60$	$40$	$100$
No Language	$60$	$40$	$100$
Total	$120$	$80$	$200$

a.

How many total outcomes are possible?

b.

$P (Music) =$

c.

$P (Language) =$

d.

$P (Music and Language) =$

e.

$P (Music|Language) =$

f.

Is scheduling of music and world language classes a set of independent events? Why or why not?

7.

	Shorts	No Shorts	Total
Hat	$10$	$50$	$60$
No Hat	$30$	$10$	$40$
Total	$40$	$60$	$100$

a.

How many total outcomes are possible?

b.

$P (Shorts) =$

c.

$P (Hat) =$

d.

$P (Shorts and Hat) =$

e.

$P (Shorts|Hat) =$

f.

Are wearing shorts and wearing a hat independent events? Why or why not?

8.

People at an amusement park were surveyed to see if they rode the roller coaster and if they had purchased a souvenir. The data is shown in the table below. Use the data to find the probabilities and respond to the following problems.

	Souvenir	No Souvenir	Total
Ride Coasters	$400$	$400$	$800$
Not Ride	$100$	$100$	$200$
Total	$500$	$500$	$1000$

a.

How many total outcomes are possible?

b.

$P (Souvenir) =$

c.

$P (Ride) =$

d.

$P (Souvenir and Ride) =$

e.

$P (Souvenir|Ride) =$

f.

Are purchasing a souvenir and riding roller coasters independent events? Why or why not?

Go

Data gathered on the shopping patterns during the months of April and May of high school students from Peanut Village revealed the following. $38 %$ of students purchased a new pair of shorts (call this event $H$ ), $15 %$ of students purchased a new pair of sunglasses (call this event $G$ ), and $6 %$ of students purchased both a pair of shorts and a pair of sunglasses.

9.

Find the probability that a student purchased a pair of sunglasses given that you know they purchased a pair of shorts.

$P (G | H) =$

10.

Find the probability that a student purchased a pair of shorts or purchased a new pair of sunglasses.

$P (H or G) =$

11.

Given that you know a student has purchased at least one of the items, what is the probability that they purchased only one of the items?

12.

Are the two events, $H$ and $G$ , independent of one another? Why or why not?

The table provided displays data collected from $200$ individuals concerning whether or not to extend the length of the school year. Use the table to respond to problems 13–15.

	For	Against	No Opinion	Total
Youth (5 to 19)	$7$	$35$	$12$
Adults (20 to 55)	$30$	$27$	$20$
Seniors (55+)	$25$	$16$	$28$
Total				$200$

13.

Given the condition that a person is an adult, what is the probability that they are in favor of extending the school year?

$P (For|Adult) =$

14.

Given the condition that a person is against extending the school year, what is the probability they are a senior?

$P (Senior|Against) =$

15.

What is the probability that a person has no opinion given that they are a youth?

$P (No Opinion|Youth) =$