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Math Help - probability

  1. #1
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    probability

    A person (xxx) wrote a phone number on a note and that was later lost. When he try to recollect, he can remember that the number had 7 digits, the digit 1 appeared in the last three places and digit 0 did not appear at all. What is the probability that the phone number contains at least two prime digits?
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  2. #2
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    This is a problem that would probably be better solved by writing down the phantom phone number along with the other information we have:

    _ _ _ - _ 1 1 1

    is the basic setup of our mystery number. We are told that there are no 0's in this number, so our "pool" of available numbers goes from 10 to 9. We are then asked, what is the PROBABILITY that of the remaining four spaces, that at LEAST two will have a prime number in them.

    Our primes in this case would be 2, 3, 5, 7. That would mean for any one space, our chances of a prime number would be \frac{4}{9}. In the case of TWO prime numbers, we would have:

    \frac{4}{9}\frac{4}{9}\frac{5}{9}\frac{5}{9}

    The question though is. . .is this the probability of at LEAST two prime numbers in our phone number? No. This is the probability of EXACTLY two prime numbers. So we need to calculate the probability of, EXACTLY three prime numbers and EXACTLY four prime numbers so that:

    P(exactly 2 prime #'s)+P(exactly 3 prime #'s)+P(exactly 4 prime #'s)=P(at least 2 prime #'s)

    See if you can grab it from here.
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