Question

You survey customers at a restaurant who have contracts with three different wireless telecommunication providers. The survey asks whether they have cell phone service at the restaurant. The results, given as joint relative frequencies, are shown in the two-way table. Find the probability that a randomly selected customer has a contract with provider B. Then find the probability that a randomly selected customer who does not have cell phone service has a contract with provider B. Write your answers as decimals rounded to the nearest hundredth. Use your answers to determine whether having a contract with provider B and not having cell phone service are independent events.

Answer 1

a)
`\text{P(provider\:B) = 0.42}\\`

b)
`\text{P(provider\:B\:} | \text{\: No) = 0.42}\\\\`

Explanation:

The joint probability table is attached below.

There are three different wireless telecommunication providers.

1. Provider A

2. Provider B

3. Provider C

The survey asks the customers whether they have cell phone service at the restaurant.

The 'Yes' and 'No' probabilities refer to the cell phone service.

a) Find the probability that a randomly selected customer has a contract with provider B.

The required probability is given by

`P(provider\:B) = 0.37 + 0.05 \\P(provider\:B) = 0.42\\`

b) Find the probability that a randomly selected customer who does not have cell phone service has a contract with provider B.

The required probability is given by

`P(provider\:B\:| \: No) = (P(provider\:B\: and \: No))/(P(No))\\\\where\\\\P(provider\:B\: and \: No) = 0.05\\\\P(No) = 0.04 + 0.05 + 0.03 \\\\P(No) = 0.12\\\\P(provider\:B\:| \: No) = (0.05)/(0.12)\\\\P(provider\:B\:| \: No) = 0.417 \\\\P(provider\:B\:| \: No) = 0.42\\\\`

Moreover, the two events having a contract with provider B and not having cell phone service are independent events since P(provider B) is equal to the P(provider B | No)