An airplane has 100 seats for passengers assume that the...

An airplane has 100 seats for passengers. Assume that the probability that a person holding a ticket appears for the flight is 0.90. If the airline sells 105 tickets, what is the probability that everyone who appears for the flight will get a seat?

Transcript

00:01 So in this video we are going to look at finding the probability that everyone who appears for the flight will get the seat.

00:10 All right? so here we will define our success as we will define our success as the probability that a person holding a ticket appears for the flight.

00:24 All right? therefore we can say that the probability of success, the, probability of success is going to be equals to point 90 and here the probability of success is basically the person holding a ticket appears for the flight all right and anything expect except this is going to be the probability of this is going to be the probability of failure which is that the person is not going to attend for the flight which is going to be equals to 1 minus 0 .90 and has this is going to be equals to 0 .10 all right so here even though it might not have looked like a binomial to start off it reduces to two outcomes on any individual trial and the two outcomes are either the person can attend the flight or not all right and if we let our random variable x okay if we like the random variable x that is going to denote that is going to denote the number of people who show up number of people who show up all right if we are going to assume x to be the number of people who show up then x has the binomial distribution then we can say that then x has bionomial distribution biomial distribution with the value of the n which is sample size to be equals to 105 why 105 because the airline has sold 105 tickets and the probability of success which is denoted by p is going to be equals to 0 .90 that stays constant from trial to trial okay and knowing what happens on one role gives us no information on what will happen on the another so the trials are also independent therefore the trials are the trials are independent and the trials are independent so the condition of binomial distribution are satisfied here okay the condition of binomial distribution are satisfied here condition of binomial distribution is satisfied here.

03:42 All right.

03:43 And since the condition is satisfied here, therefore we need to calculate the probability we can put this into our binomial formula.

03:52 And according to the binomial formula, we know that the probability that capital x is going to be equals to x is given by n choose x times p to the power of x, all right, which is basically times the key times the q which is the probability of failure here probability of failure all right raised to the power total number of failure so the total number of failure failure is going to be n minus x now we are going to substitute the variant calculate our required probability all right so basically here it has been given that n is equal to 105 the x is going to be equals to nothing but 100 the value of the p is given as 0 .90 the value of the q is given as 0 .10 and what we are supposed to calculate is what will be the probability that the value of the x is going to be less than or equals to hundred all right and this can be written as 1 minus the probability that x is going to be greater than 100 okay which in turns equals to 1 minus the probability that x is equals to 1 .01 plus the probability that x is equal to 102 all right plus the probability that x is equals to 103 plus the probability that x is equals to 104 and at last the probability that x is equals to 105 all right now we have to solve each of this probability in order to get our required answer so here i'm going to solve it let me show a case then we will do the rest as exactly.

05:51 So the probability that x is equals to 101 is given by 105 c101 times probability of success which is 0 .9 to the power 101 times the probability of failure to the power 105 minus 101 which is 4...

Question

An airplane has 100 seats for passengers. Assume that the probability that a person holding a ticket appears for the flight is 0.90. If the airline sells 105 tickets, what is the probability that everyone who appears for the flight will get a seat?

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