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Math Help - Probability Problem

  1. #1
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    Probability Problem

    Dear Colleagues,

    I have the following question and hope to help me to solve it.

    You randomly choose two days of a week for your holiday.
    What's the probability that you chose Saturday and Sunday?


    Best Regards,
    Raed.
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  2. #2
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    Re: Probability Problem

    P("\text{Saturday and Sunday}")=\frac{2}{7}\cdot \frac{1}{6}
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  3. #3
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    Re: Probability Problem

    Quote Originally Posted by Ridley View Post
    P("\text{Saturday and Sunday}")=\frac{2}{7}\cdot \frac{1}{6}
    Thank you very much for your reply. But from yesterday up to now I try to understand the answer and I do not.


    Regards,
    Raed.
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  4. #4
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    Re: Probability Problem

    The probability of selecting either Saturday or Sunday as the first pick is (since the two events are disjoint): 1/7 + 1/7 = 2/7

    Once you picked one of them for the first pick, you're left with six days and only one favorable outcome, so the probability of selecting the remaining day is 1/6.
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  5. #5
    Super Member ILikeSerena's Avatar
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    Re: Probability Problem

    Here's another way to look at it.

    The number of ways to pick 2 (different) days from a week is \binom 7 2.
    There is only 1 favorable outcome (in which you pick Saturday and Sunday).

    P(\textrm{Saturday and Sunday}) = {\textrm{number of favorable outcomes} \over \textrm{total number of outcomes}} = {1 \over \binom 7 2} = {2 \cdot 1 \over 7 \cdot 6}.
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