Consider a bar that has a limited capacity of 30 people. The bar has an entrance fee of $5/person. People arrive to this bar at a rate of 4/hour. The time each person spends in the bar follows an exponential distribution with rate µ. Suppose it costs 3µ per hour for this bar to provide service to the customers. Find µ that maximizes the benefit of this bar.

a. she will receive a refund of $278.

step-by-step explanation:

step-by-step explanation:

what are you trying to solve here

step-by-step explanation:

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560