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Thread: lottery ticket problem

  1. #1
    Actuary.com - Level II Poster
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    lottery ticket problem

    ok, Lottery tickets have 4 digits and they go from 0000 to 9999. There are therefore 10,000 different tickets. Suppose you buy a ticket. what is the probability you match only the last two digits of the winning ticket?

  2. #2
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    I believe this is how its done:

    P(matching only the last two) = P(match the last two) - P(match the last three) - P(match all four)

    1/100 - 1/1000 - 1/10000 = (100-10-1)/10000= 89/10000

  3. #3
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    Isn't it just P(not matching first) x P(not matching second) x P(matching third) x P(matching fourth) = 9/10 x 9/10 x 1/10 x 1/10 = 81/10000?

  4. #4
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    Thanks guys...... The actex book says its 90/10000........ it says that the thousand place can be any of 10 numbers and that the 100 place can be any 9 making 90 total....... I thought it was 81 too.....9 wrong for the first and 9 wrong for the second digit.

  5. #5
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    I dont get how the 1000 place can be any of 10 numbers because then 1 number would match the winning??

  6. #6
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    Any answers? Is the book wrong?

  7. #7
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    according to your answer, here is what I think (guess):

    first divide this set into two parts, the first two digits and last two digits.

    1. the probability of matching the last two digits is 1/100.

    2. either matching the first or second digit fails to fulfill your goal to match the last two digits only. Therefore, this part is 10/10 * 9/10

    then 9/10 * 1/100 = 90/10000

    Can someone be able to explain it?

  8. #8
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    Wouldn't that imply that there is a 100% chance that you fail to match the first digit? I sure don't want to play that lottery.

  9. #9
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    I mean either first or second digit matched is considered as a failure in this question. (once one of the first two digits is matched, you don't need to match another one to be failed.)

  10. #10
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    Is it possible for you to write out word for word the acetex solution? I remember this problem and I know I figured out what they meant, but I've forgotten how.

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