# Probability Question #1

#### curious engineer

2. The phone lines to an airline reservation system are occupied 40% of the time. Assume that the events that the lines are occupied on successive calls are independent. Assume that 10 calls are placed to the airline.
What is the expected number of calls in which the lines are all occupied

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For a binomial distribution, $$\displaystyle E[X] = np.$$ where n is the number of trials and p is the probability of success (in this case the probability the lines are occupied)
$$\displaystyle E[X] = np = 10*.4 = 4$$