Question

unit 10 lesson 6

1. 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
not ride	100	100	200
	500	500	1000

a. how many total outcomes are possible?

b. $p(\text{souvenir}) = \frac{500}{1000}$

c. $p(\text{ride}) = \frac{800}{1000}$

d. $p(\text{souvenir and ride}) = \frac{400}{1000}$

e. $p(\text{souvenir|ride}) = \frac{400}{800}$

f. are purchasing a souvenir and riding roller coasters independent events? why or why
not?

Explanation:

Part a

Step1: Identify total from table

The table's bottom - right cell (Total row and Total column) gives the total number of surveyed people.
From the table, the total number of outcomes (total number of people surveyed) is 1000.

Step1: Recall probability formula

The probability of an event \(A\), \(P(A)=\frac{\text{Number of favorable outcomes for }A}{\text{Total number of outcomes}}\). For \(P(\text{Souvenir})\), the number of people who purchased a souvenir is 500 (from the "Souvenir" column total), and the total number of outcomes is 1000.

Step2: Calculate the probability

\(P(\text{Souvenir})=\frac{500}{1000}=\frac{1}{2}\)

Step1: Recall probability formula

For \(P(\text{Ride})\), the number of people who rode coasters is 800 (from the "Ride Coasters" row total), and the total number of outcomes is 1000.

Step2: Calculate the probability

\(P(\text{Ride})=\frac{800}{1000}=\frac{4}{5}\)

Answer:

1000

Part b