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Math Help - How shld i go about doing this qn????

  1. #1
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    How shld i go about doing this qn????

    Hi, i have the following question that i cant solve for days:

    A small commuter airline flies plane that can seat up to eight passengers. The airline has determined that the probability that a ticketed passenger will not show up for a flight is 0.2. For each flight, the airline sells tickets to the first ten people placing orders. The probability distribution for the number of tickets sold per flight is shown in the accompanying table. For what proportion of the airline's flights does the number of ticketed passengers showing up exceeds the number of available seats? (Assume independence between number of tickets sold and that a ticketed passenger will show up).

    Number of tickets 6 7 8 9 10
    Probability 0.30 0.30 0.25 0.10 0.05

    Thanks a lot for anyone who can help me through this problem!!!!!
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  2. #2
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    Quote Originally Posted by etjh View Post
    Hi, i have the following question that i cant solve for days:

    A small commuter airline flies plane that can seat up to eight passengers. The airline has determined that the probability that a ticketed passenger will not show up for a flight is 0.2. For each flight, the airline sells tickets to the first ten people placing orders. The probability distribution for the number of tickets sold per flight is shown in the accompanying table. For what proportion of the airline's flights does the number of ticketed passengers showing up exceeds the number of available seats? (Assume independence between number of tickets sold and that a ticketed passenger will show up).

    Number of tickets 6 7 8 9 10
    Probability 0.30 0.30 0.25 0.10 0.05

    Thanks a lot for anyone who can help me through this problem!!!!!

    The probability that a passenger does show up is 0.8

    The probability that 9 tickets are sold and all passengers 9 show up = 0.8(0.1)

    This situation will cause a rejected passenger.

    If 10 tickets are sold and all 10 passengers show up, 2 passengers will be rejected.

    If 10 tickets are sold and any 9 of these 10 passengers show up, 1 passenger gets rejected.

    There are \binom{10}{9} ways that 9 of the 10 can show up, which is the same as saying that there are 10 ways 1 passenger doesn't show up.

    You must add all probabilities together to find the probability of rejection.
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