Question

learning goal from lesson 19.4
can construct and interpret two - way frequency tables of data
when two categories are associated with each object. i can
determine independence of events using a two - way table as a
sample space. i can approximate conditional probabilities using a
two - way table as a sample space.
lesson reflection (circle one)
starting... getting there... got it!
lesson 19.4 checkpoint
once you have completed the above problems and checked your solutions, complete the lesson checkpoint
below.
complete the lesson reflection above by circling your current understanding of the learning goal.
the table shown shows the results of a customer satisfaction survey for a cellular service provider, by
location of the customer. in the survey, customers were asked whether they would recommend a plan
with the provider to a friend.
one of the customers that was surveyed was chosen at random.

1. what is the probability that the customer was from parkville?
2. what is the probability that the customer was from parkville and satisfied?
3. what is the probability that the customer was from parkville or satisfied?

Explanation:

Step1: Probability formula

The probability formula is \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\)

Step2: Probability that the customer was from Parkville

The number of customers from Parkville is \(47\) (from the total column of Parkville). The total number of customers is \(150\). So \(P(\text{Parkville})=\frac{47}{150}\)

Step3: Probability that the customer was from Parkville and satisfied

The number of customers from Parkville and satisfied is \(41\). Using the probability formula \(P(\text{Parkville and Satisfied})=\frac{41}{150}\)

Step4: Probability that the customer was from Parkville or satisfied

Use the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)
\(P(\text{Parkville})=\frac{47}{150}\), \(P(\text{Satisfied})=\frac{116}{150}\), \(P(\text{Parkville and Satisfied})=\frac{41}{150}\)
\(P(\text{Parkville or Satisfied})=\frac{47 + 116- 41}{150}=\frac{122}{150}=\frac{61}{75}\)

Answer:

1. \(\frac{47}{150}\)
2. \(\frac{41}{150}\)
3. \(\frac{61}{75}\)