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26 August, 02:06

Exclude leap years from the following calculations. (a) Compute the probability that a randomly selected person does not have a birthday on March 14. (b) Compute the probability that a randomly selected person does not have a birthday on the 2 nd day of a month. (c) Compute the probability that a randomly selected person does not have a birthday on the 31 st day of a month. (d) Compute the probability that a randomly selected person was not born in February.

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  1. 26 August, 02:07
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    a) 99.73% probability that a randomly selected person does not have a birthday on March 14.

    b) 96.71% probability that a randomly selected person does not have a birthday on the 2 nd day of a month.

    c) 98.08% probability that a randomly selected person does not have a birthday on the 31 st day of a month.

    d) 92.33% probability that a randomly selected person was not born in February.

    Step-by-step explanation:

    A probability is the number of desired outcomes divided by the number of total outcomes.

    A non-leap year has 365 days.

    (a) Compute the probability that a randomly selected person does not have a birthday on March 14.

    There are 365-1 = 364 days that are not March 14. So

    364/365 = 0.9973

    99.73% probability that a randomly selected person does not have a birthday on March 14.

    (b) Compute the probability that a randomly selected person does not have a birthday on the 2 nd day of a month.

    There are 12 months, so there are 12 2nds of a month.

    So

    (365-12) / 365 = 0.9671

    96.71% probability that a randomly selected person does not have a birthday on the 2 nd day of a month.

    (c) Compute the probability that a randomly selected person does not have a birthday on the 31 st day of a month.

    The following months have 31 days: January, March, May, July, August, October, December.

    So there are 7 31st days of a month during a year.

    Then

    (365-7) / 365 = 0.9808

    98.08% probability that a randomly selected person does not have a birthday on the 31 st day of a month.

    (d) Compute the probability that a randomly selected person was not born in February.

    During a non-leap year, February has 28 days. So

    (365-28) / 365 = 0.9233

    92.33% probability that a randomly selected person was not born in February.
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