1. ## probability

There is a plane with $50$ seats, and $55$ passengers have tickets. Define $Y$ as the number of ticketed passengers who actually show up for the flight. Here is the pmf:

$y = 45, 46 ,47, 48, 49, 50, 51, 52, 53, 54, 55$
$p(y) = 0.05, 0.1, 0.12, .14, .25, 0.17, .06, .05, 0.03, 0.02, 0.01$

(a) what is probability that flight will accommodate all ticketed passengers who show up?

So this is $p(55) = 0.01$?

(b) what is the probability that not all ticketed passengers who show up can be accommodated?

so this is $1 - p(55) = 0.99$?

(c) If you are first person on a standby list (which means you will be the first one to get on the plane if there are any seats available after all ticketed passengers have been accommodated), what is the probability that you will be able to take the flight? if you are the third person on the standby list?

so all $50$ seats cant be filled?

2. Originally Posted by heathrowjohnny

$y = 45, 46 ,47, 48, 49, 50, 51, 52, 53, 54, 55$
$p(y) = 0.05, 0.1, 0.12, .14, .25, 0.17, .06, .05, 0.03, 0.02, 0.01$

(a) what is probability that flight will accommodate all ticketed passengers who show up?

(b) what is the probability that not all ticketed passengers who show up can be accommodated?

(c) If you are first person on a standby list (which means you will be the first one to get on the plane if there are any seats available after all ticketed passengers have been accommodated), what is the probability that you will be able to take the flight? if you are the third person on the standby list?

(a) what is probability that flight will accommodate all ticketed passengers who show up?

You need P(Y<=50)=0.05+ 0.1+ 0.12+ 0.14+ 0.25+ 0.17

(b) what is the probability that not all ticketed passengers who show up can be accommodated?

Yes this is 1 - (your answer to part a)

(c) If you are first person on a standby list (which means you will be the first one to get on the plane if there are any seats available after all ticketed passengers have been accommodated), what is the probability that you will be able to take the flight? if you are the third person on the standby list?

If you're first on the list you'll get on the flight if 49 or fewer turn up.

If you're third on the list you'll get on the flight if 47 or fewer turn up.