Answer:
a. The probability that the aircraft is fully occupied = 0.3642
b. The probability that between 1 and 5 (including 1 and 5) passengers do not show up is = 0.6354
Explanation:
From the given information:
We are to compute the probability that:
a. The aircraft is fully occupied( i.e. all the passengers show up)
b. Between 1 and 5 (including 1 and 5) passengers do not show up
Given that:
Percentage of passengers that do not show up = 2% = 0.02
And the population of the passengers = 50; since 50 tickets are being sold for a specific flight.
Let assume X be the random variable that follows a binomial distribution, thus, the number of passengers from the aircraft with 50 passengers can be represented as:

Thus;
The probability that the aircraft is fully occupied i.e. all the passengers show up is:

= 0.98⁵⁰
= 0.3642
Hence, The probability that the aircraft is fully occupied = 0.3642
b. The probability that between 1 and 5 (including 1 and 5) passengers do not show up is:
= P(X = 1) + P(X =2) + P(X = 3) + P(X = 4) + P(X = 5)
=


= 0.6354
Hence, The probability that between 1 and 5 (including 1 and 5) passengers do not show up is = 0.6354