MATH 350 Quiz 05

1. Suppose you own a store with two air conditioners, one for the main office and one for the back shop. The probability the the main office air conditioner requires a service call is $\mathbb{P}[M] = 0.22$. The probability that the back shop air conditioner requires a service call is $\mathbb{P}[B] = 0.15$.
   1. It is reasonable to assume the two air conditioners are independent. Provide a justification for why it is reasonable to assume that the two air conditioners are independent.
   2. What is the probability that both air conditioners need a service call?
   3. What is the probability that neither air conditioner needs a service call?
2. Suppose both the air conditioners have the same probability of requiring a service call, say probability $p$.
   1. What distribution could you use to model the probabilities associated with some number of the air conditioners needing a service call?
   2. What is the probability that at least one air conditioners need a service call?
   3. What is the probability that neither air conditioner needs a service call?