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Math Problem - Can anyone solve this probability problem?

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  • 22-01-2013 5:27pm
    #1
    Leaving Cert Student
    Registered Users Posts: 1,026 ✭✭✭


    In the National Lottery, forty five balls numbered 1 to 45 are placed in a drum.
    Six balls are taken at random from the drum as the winning combination.
    If you select six numbers from 1 to 45, what is the probability that, at most,
    only one of them matches with the winning combination?
    Give your answer in decimal form, correct to two decimal places.


    Answer: 0.82
    Tagged:


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    #2
    Leaving Cert Student
    Registered Users Posts: 1,026 ✭✭✭Leaving Cert Student


    anyone show how to get this answer please?


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    #3
    TheChizler
    Registered Users Posts: 9,437 ✭✭✭TheChizler


    Can you show what you've got so far?


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    #4
    Leaving Cert Student
    Registered Users Posts: 1,026 ✭✭✭Leaving Cert Student


    TheChizler wrote: »
    Can you show what you've got so far?

    I don't know how to do it to be honest. All I have done is 45C6 and it gives approx 8 million different ways of choosing 6 from 45 so I assume thats the total. What to do after that is puzzling me...?


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    #5
    Derpington95
    Registered Users Posts: 269 ✭✭Derpington95


    We havent done that chapter yet but ill try help.
    Doing 45C6 means there are 8145060 possible combinations disregarding order. Say the winning number consisted of a,b,c,d,e,f
    These 6 numbers can be arranged in 6! (720) winning ways.
    So you must find out the odds of those 6 numbers coming up in any order multiplied by the odds of picking one number of the 6 Probably worng but at least i tried :P? Thats what i'm guessing we havent done that yet since im only a smelly 5th year ;)


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    #6
    Leaving Cert Student
    Registered Users Posts: 1,026 ✭✭✭Leaving Cert Student


    Ok I got help off my teacher for this one thank you very much for your reply derpington a true gentleman :).

    The way you'd do this is get the total as you said 45 C6.
    Then get the total ways of getting zero: 39c6
    and the total ways of getting 1: 39C5 X 6C1

    Add the latter two results and divide by the total number of ways to get .82 :)


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