Each year, a company either makes a profit or takes a loss. If the company made a profit the year before, they will make a profit with probability 0.7. If they took a loss the year before, they will make a profit with probability 0.3. What is the long-run probability the company will make a profit? ...

Assume that the business makes a profit with probability 0.8 in the first year. For each year thereafter, the business makes a profit with probability 0.9 if it made a profit in the previous year, and with probability 0.2 if it did not make a profit in the previous year. What is the probability that the business makes a profit in exactly two of its first three years?

Dave catches a bus to school. If he catches the 7am bus, then he will arive at school on time with probability 0.95. If he misses the 7am bus, then he will arrive on time at school with probability 0.1. Suppose the probability of him catching the 7am bus is 18. 0.8. Find the probability that he will arrive on time at school. If he arrived on time at school today, what is the probability that he caught the a. b. 7am bus?

In general after group makes a reservation in a restaurant they do not show up 20% of the time. If a restaurant has six reservations for the evening, what is the probability that exactly 2 do not show up? 

Assume that the business makes a profit with probability 0.7 in the first year. For each year thereafter, the business makes a profit with probability 0.9 if it made a profit in the previous year, and with probability 0.3 if it did not make a profit in the previous year. What is the probability that the business makes a profit in exactly two of its first three years?

In general, after a group makes a reservation at a restaurant, they do not show up 20% of the time. If a restaurant has 8 reservations for the evening, what is the probability that more than two do not show up?

Assume that the business makes a profit with probability 0.4 in the first year. For each year thereafter, the business makes a profit with probability 0.9 if it made a profit in the previous year, and with probability 0.2 if it did not make a profit in the previous year. What is the probability that the business makes a profit in exactly two of its first three years?

The probability that an applicant will be approved for a mortgage is 0.15. Each applicant has the same probability of being approved and the event that they are approved are independent. What is the probability that out of three applicants, exactly two of them get approved? Enter your answer as a decimal, with three decimal places. For example, if the probability is 15.37%, enter 0.154

Assume that the business makes a profit with probability 0.5 in the first year. For each year thereafter, the business makes a profit with probability 0.9 if it made a profit in the previous year, and with probability 0.4 if it did not make a profit in the previous year. What is the probability that the business makes a profit in exactly two of its first three years?

A company receives 30% of its shipments from source A and the rest from source B. For source A, the defective rate is 10% and for source B, the defective rate is 6%. The company just receives a shipment which contains 10 items.Determine the probability that there will be one defective item.