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Math Help - Lottery Probability Question

  1. #1
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    Lottery Probability Question

    Ok, i need a maths genius to help me out, (I'm a dumb blonde).

    probability Question to do with a lottery draw.



    Pot has 49 numbers from 1 -49

    six numbers are drawn.

    I have two tickets:

    Q1: What is the probability of winning if the two tickets have completely different numbers on them

    Q2: What is the probability of winning if the two tickets have 4 numbers that are identical on each of the tickets.

    Q3: If the numbers on the two tickets were picked at random, What is the probability of picking 1 number identical
    on each of the two tickets.

    Q4: If the numbers on the two tickets were picked at random, What is the probability of picking 4 numbers identical
    on each of the two tickets.

    Q5: If the numbers on the two tickets were picked at random, What is the probability of picking any numbers
    identical on each of the two tickets.

    Q6: If the numbers on the two tickets were picked at random, What is the probability of picking no numbers
    identical on each of the two tickets.

    Any help would be greatly appreciated

    Cheers,

    Claire.
    xxx
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  2. #2
    MHF Contributor
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    Re: Lottery Probability Question

    Hey clairescanlon.

    Can you show us what you tried?

    Hint for first one: The total number of possibilities for the number of permutations of tickets is 49*48*47*46*45*44. If you have different numbers on both then it means that you will have less possibilities since they can't over-lap.

    This translates into the second set having only 43 choices to start since we can't duplicate the numbers in the first and this means we have 43*42*41*40*39*38 possible permutations if we can't repeat numbers.

    So these events are disjoint so we add up the probabilities to get the total of 1/(49*48*47*46*45*44) + 1/(43*42*41*40*39*38)

    The above assumes that you need to get all numbers correct to win: if this is not the case then you need to point this out.
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