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Math Help - probability

  1. #1
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    probability

    What is the probability that a 6-digit phone number contains at least one 2? (Repetition of numbers and lead zero are allowed).
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  2. #2
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    Imagine the situation as being a room with 6 phones. Each phone has 10 digits on it, and you have to pick one digit from each phone!

    As such there are 10 different ways you can choose 1 from 10. And you have to choose 6 of these. Hence there are  10^6 combinations!

    Now lets consider the same situation, only now all the 2s on the phones have been removed. So now there are 6 phones, each with only 9 digits, (0,1,3,4,5,6,7,8,9). So you are choosing 1 button from 9, 6 times! Hence  9^6.

    So we have concluded that there are 10^6 combinations, and  9^6 of them have no 2!

    Hence the probability that there is at least one 2 is :

     10^6 - 9^6  = 468559
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  3. #3
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    The response is attached as a gif image, hope this helps you.
    Attached Thumbnails Attached Thumbnails probability-prob1.gif  
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