an airline has a policy of booking as many as 16 persons on an airplane that can seat only 5. (past studies have revealed that only 94% of the booked passengers actually arrive for the flight.) find the probability that if the airline books 16 persons, not enough seats will be available. Is it unlikely for such an overbooking to occur? What would be that probability.
i am so confused it says 94% of the booked passengers arive so that means they will always have a overbook. someone else needs to help you. sorry i cant. my college is closing and i have to leave but i glanced over your question.
*it was supposed to say 15, not 5 persons..
ok, thanks...
could someone else please help.
+23254 If you have a calculator that handles combinations -- that is, you can calculate expressions such as 16C3, the combinational value of 16 items taken 3 at a time -- you can do it like this:
The probability of having enough space is calculated as follows:
16C0 · (.94)^0 · (.06)^16 (nobody shows up)
16C1 · (.94)^1 · (.06)^15 (1 person shows up)
16C2 · (.94)^2 · (.06)^14 (2 persons show up)
16C3 · (.94)^3 · (.06)^13 (3 persons show up)
16C4 · (.94)^4 · (.06)^12 (4 persons show up)
16C5 · (.94)^5 · (.06)^11 (5 persons show up)
Sum these 6 values; this will give you the probability that everyone gets seated.
Overbooking would be the opposite, so subtract that answer from 1.000, to get the probability that overboooking occurs.
+130477 Very nice geno......I'm glad we have some people who can handle probability questions....I can do a few, but generally, it's not my strongpoint (if I even have one !!!)...........
I do not have a calcuator on me...am using one found on google..but i've been doing the calculations wrong. Thank you for your help! Have a few more..that are worded differently..hmm
+23254 Let me modify my answer to represent having the plane hold 15 passengers:
The only way to overbook is for all 16 persons to show up; this will occur only if first persons shows up, the second person shows up, etc.
This has a probability of (.94) x (.94) x ... x (.94) all sixteen times, which is (.94)^16.
Find that value, that is the probability of having 16 out of 16 persons showing up.
