An airline has a policy of booking as many as 17 persons on an airplane that can seat only 16. (Past studies have shown that only 89% of the booked passengers actually arrive for a flight.) Find the probability that if an airline books 17 persons, not enough seats will be available.

Please tell me how to work this out.

Sorry, forgot the last line - Find the probability that not enough seats will be available.

To find the probability that if an airline books 17 persons, not enough seats will be available, we can break it down into two steps:

Step 1: Calculate the probability that all 17 persons will show up for the flight.
Step 2: Calculate the probability that 17 persons show up, given that all 17 persons were booked and the probability of each person showing up is the value from Step 1.

Step 1:
Since past studies have shown that only 89% of the booked passengers actually arrive for a flight, the probability that any single person will show up for the flight is 0.89. Therefore, the probability that all 17 persons will show up is:
P(all 17 show up) = (0.89)^17

Step 2:
Given that all 17 persons were booked, we assume that the airline does not allow for any last-minute cancellations or changes to the passenger list. Therefore, if all 17 persons show up, there will not be enough seats available.

Therefore, the probability that if an airline books 17 persons, not enough seats will be available is the same as the probability that all 17 persons show up:
P(not enough seats) = (0.89)^17

Using a calculator, the probability P(not enough seats) is approximately 0.203, or 20.3%.

To find the probability that if an airline books 17 persons, not enough seats will be available, we need to consider two scenarios:

1. All 17 passengers arrive for the flight.
2. Fewer than 17 passengers arrive for the flight.

Let's calculate these probabilities step by step:

Step 1: Calculate the probability that all 17 passengers arrive for the flight.
The probability that a passenger arrives for the flight is given as 89%, which means that the probability a passenger does not arrive is 100% - 89% = 11%.

To find the probability that all 17 passengers arrive, we multiply the probability of each passenger's arrival or non-arrival:
P(all 17 arrive) = (0.89)^(17)

Step 2: Calculate the probability that fewer than 17 passengers arrive for the flight.
The probability that fewer than 17 passengers arrive is the complement of all 17 passengers arriving:
P(fewer than 17 arrive) = 1 - P(all 17 arrive)

Now, let's calculate these probabilities:

P(all 17 arrive) = (0.89)^(17) ≈ 0.1501
P(fewer than 17 arrive) = 1 - 0.1501 ≈ 0.8499

Therefore, the probability that if an airline books 17 persons, not enough seats will be available is approximately 0.8499 or 84.99%.

ok, then the question is what is the probability of all 17 wanting seats?

Pr(all)=.89^17

Pr not enough seats=Pr(all)