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Math Help - numbers + probability

  1. #1
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    numbers + probability

    What is the probability that a two digit number chosen at random will be a multiple of 3 and not of 5 .
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  2. #2
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    Quote Originally Posted by mathaddict View Post
    What is the probability that a two digit number chosen at random will be a multiple of 3 and not of 5 .
    One way is just to write out all two digit numbers that are multiples of 3 and cross out those that are also a multiple of 5 .... How many are there ....? Now divide by the total number of two digit numbers.
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    Hello, mathaddict!

    What is the probability that a two digit-number chosen at random
    will be a multiple of 3 and not of 5?

    There are 90 two-digit numbers.

    One-third of them are mutliples of 3: . \frac{90}{3} \:=\:30 multiples of 3.

    But every fifth one of them is a multiple of 5: . \frac{30}{5} \:=\: 6 multiples of 15.

    Hence, there are: . 30 - 6 \:=\:{\color{blue}24} multiples of 3 which are not multiples of 5.


    Therefore: . P(\text{multiple of 3, not 5}) \:=\:\frac{24}{90} \:=\:\frac{4}{15}

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