Answer:
a) [tex]\text{P(provider\:B) = 0.42}\\[/tex]
b) [tex]\text{P(provider\:B\:} | \text{\: No) = 0.42}\\\\[/tex]
Step-by-step 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
[tex]P(provider\:B) = 0.37 + 0.05 \\P(provider\:B) = 0.42\\[/tex]
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
[tex]P(provider\:B\:| \: No) = \frac{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) = \frac{0.05}{0.12}\\\\P(provider\:B\:| \: No) = 0.417 \\\\P(provider\:B\:| \: No) = 0.42\\\\[/tex]
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)
