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24 April, 23:53

An airline estimates that 90% of its eastbound flights arrive on time and 72% of its westbound flights arrive on time. This morning, 42% of the airline's schedule is westbound flights. If a flight is chosen at random, what is the probability that the flight does not arrive on time? Write your answer as a percent rounded to the nearest tenth.

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  1. 25 April, 00:11
    0
    Probability that the flight doesn't arrive on time = 0.2 (to the nearest tenth)

    Step-by-step explanation:

    90% of the eastbound flights arrive on time, i. e. Pe = 0.9

    10% of the eastbound flights do not arrive on time, Qe = 1 - 0.9 = 0.1

    72% of the westbound flights arrive on time, i. e. Pw = 0.72

    28% of the westbound flights do not arrive on time, Qw = 1 - 0.72 = 0.28

    42% of the airline schedule this morning is westbound (i. e 58% is eastbound)

    If a flight is chosen at random:

    Probability that it is a westbound flight and it does not arrive on time = 0.28 * 0.42 = 0.1176

    Probability that it is an eastbound flight and it does not arrive on time = 0.1 * 0.58 = 0.058

    Probability that the flight doesn't arrive on time = 0.1176 + 0.058

    Probability that the flight doesn't arrive on time = 0.1756

    Probability that the flight doesn't arrive on time = 0.2 (to the nearest tenth)
  2. 25 April, 00:22
    0
    The probability, that a flight does not arrive on time is 18.4%

    Step-by-step explanation:

    Here we have that;

    The percentage of the Eastbound flight that arrive on time = 90%

    The percentage of the Westbound flight that arrive on time = 72%

    The percentage of Westbound flights the present morning = 42%

    Therefore, the percentage of Eastbound flights the present morning = 100% - 42% = 58%

    Hence the probability, p, that a flight will arrive on time this morning is given as follows

    0.9 * 0.58 + 0.72 * * 0.42 = 0.816

    Hence the probability, q, that a flight does not arrive on time = 1 - p

    Which gives, q = 1 - 0.816 = 0.184

    To convert back to percentage, we multiply by 100 hence;

    0.184 * 100 = 18.4%

    The probability, that a flight does not arrive on time = 18.4%.
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