# Probability that a flight is over-booked

#### anthmoo

An airline has 300 seats available on a flight to Australia. It is known from experience that on average only 99% of those who have booked seats actually arrive to the flight, the remaining 1% being called "no-shows". The airline therefore sells more than 300 seats. If more than 300 passengers then arrive, the flight is over-booked. Assume that the number of no-show passengers can be modelled by a binomial distribution.

Question
1) If the airline sells 303 seats:
i)State a suitable distribution for the number of no show passengers and state a suitable approximation to this distribution, giving the values of any parameters.
ii) Show that the probability that the flight is over-booked is 0.4165, correct to 4 decimal places.

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If anyone can help on this question please do because it's really annoying me as for part ii) especially, I keep the complimentary probability instead of the actual one and I have no idea where i'm going wrong! >_<

#### Plato

MHF Helper
If the airline sells 303 tickets and 301, 302, or 303 ticket holders actually show up for a flight then that flight will be over-sold. The probability that it happens is $$\displaystyle \sum\limits_{k = 301}^{303} {{{303} \choose k}\left( {.99} \right)^k \left( {0.01} \right)^{303 - k} } = 0.41534$$.

As you see, that answer is slightly off from the one given.

anthmoo

#### anthmoo

Ah thankyou - I understand now.

The question used a poisson approximation for this but yours is more correct

Thankyou! Plato!