Question

finding a conditional probability

a phone company surveys a sample of current customers to determine if they use their phones most often to text or use the internet. they sort the data by payment plans, as shown below.

• plan a: 27 text, 21 internet
• plan b: 13 text, 10 internet

answer the questions to determine a conditional probability.

how many customers are on payment plan b?
customers

how many of the customers on plan b text?
customers

what is the probability that a randomly selected customer who is on plan b uses the phone most often to text? give the answer in fraction form.

Explanation:

Calculate total customers on Plan B

Using the Favorable Outcomes knowledge point

$$ \text{Total on Plan B} = 13 \text{ (text)} + 10 \text{ (Internet)} = 23 $$

Identify Plan B customers who text

Using the Favorable Outcomes knowledge point

$$ \text{Plan B and text} = 13 $$

Calculate the conditional probability

Using the Theoretical Probability knowledge point

$$ P(\text{text} \mid \text{Plan B}) = \frac{\text{Plan B and text}}{\text{Total on Plan B}} = \frac{13}{23} $$

Answer:

Question 1

How many customers are on payment plan B?
<blank>23</blank> customers

Question 2

How many of the customers on plan B text?
<blank>13</blank> customers

Question 3

What is the probability that a randomly selected customer who is on plan B uses the phone most often to text? Give the answer in fraction form.
<blank>\(\frac{13}{23}\)</blank>