The probability that an airline will have to award a 2 or more discounts a month. .

Question

What is the probability that an airline will have to award 2 or more discounts a month? Given that there are 20 passengers on a plane and give awards to a pair of matching birthdays. There are 6 flights daily. The probability of having a matching pair on a flight is .4062. This is all assuming that there are 365 days in a year exactly.

Answer 1

Let p = 0.4062.

 

 

For each day, P(x ≥ 2) = P(2) + P(3) + P(4) + P(5) + P(6)

 

= p² + p³ + p⁴ + p⁵ + p⁶ = 0.275 for the probability of awarding 2 or

 

more discounts.

 

 

The probability of not awarding a discount per day is 1 - P(x ≥ 2) = 0.625.

 

 

The probability of not awarding two or more discounts in a month is 0.625^365/12 = 6 x 10^-7.

 

So the probability of awarding two or more discounts is almost a certainty: 1 - (6 x 10^-7).