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Probability 2 numbers in national lottery

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  • 04-10-2018 3:18pm
    #1
    KBD85
    Registered Users Posts: 123 ✭✭


    In the national lottery there are 47 numbers.

    If you pick 2 numbers (10 and 11)

    What is the probability that you will match both numbers

    (a) in first 6 numbers - i.e excluding bonus ball

    (b) in first 7 numbers - including bonus ball

    Can you explain your workings please?


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    #2
    Pelvis
    Closed Accounts Posts: 1,758 ✭✭✭Pelvis


    Do your own homework!


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    #3
    KBD85
    Registered Users Posts: 123 ✭✭KBD85


    Pelvis wrote: »
    Do your own homework!

    Not quite. Hope your day improves buddy.


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    #4
    tsue921i8wljb3
    Closed Accounts Posts: 5,017 ✭✭✭tsue921i8wljb3


    KBD85 wrote: »
    In the national lottery there are 47 numbers.

    If you pick 2 numbers (10 and 11)

    What is the probability that you will match both numbers

    (a) in first 6 numbers - i.e excluding bonus ball

    (b) in first 7 numbers - including bonus ball

    Can you explain your workings please?

    The probability of

    a) C(45,4)/C(47,6) so ~0.01387604

    b) C(45,5)/C(47,7) so ~0.019426456

    In the formulae above, C(n,k) is the number of different ways (combinations) you can pick k elements from a set of n elements. In a) the denominator represents how many possible six-numbers draw you can have. The numerator are your favourable cases: in order to win, the draw must contain your two numbers plus any four from the remaining 45.

    It is interesting to compare the true probability with odds offered by bookmakers.

    For a) the true odds are ~71/1 while a high street bookie is offering 60/1.

    For b) the true odds are ~50/1 while the bookie offers only 40/1.


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    #5
    KBD85
    Registered Users Posts: 123 ✭✭KBD85


    To put your workings into words for (a)

    C(45,4)/C(47,6)

    Have you got the number of combinations where it excludes both my numbers and divided it by the total number of possible combinations?

    The first part C(45,4) is what exactly?

    Thanks.


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    #6
    tayto lover
    Registered Users Posts: 51,485 ✭✭✭✭tayto lover


    60/1 for two numbers out of 6 in most bookies.


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    #7
    tsue921i8wljb3
    Closed Accounts Posts: 5,017 ✭✭✭tsue921i8wljb3


    KBD85 wrote: »
    To put your workings into words for (a)

    C(45,4)/C(47,6)

    Have you got the number of combinations where it excludes both my numbers and divided it by the total number of possible combinations?

    The first part C(45,4) is what exactly?

    Thanks.

    Exactly.

    It's explained in

    https://en.m.wikipedia.org/wiki/Lottery_mathematics

    under "Odds of getting other possibilities in choosing 6 from 49"

    So for a) the numerator is the number of ways to select the winning numbers multiplied by the number of ways to select the losing numbers.

    You must get exactly 2 numbers so number of ways to chose is C(2,2) i.e. 1

    C(45,4) is the number of ways to select the losing numbers.

    So 1 * C(45,4) is the numerator.


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    #8
    KBD85
    Registered Users Posts: 123 ✭✭KBD85


    tayto lover wrote: »
    60/1 for two numbers out of 6 in most bookies.

    That's not the correct probability though. The bookie has an edge or overround factored into those odds.

    I'm using this example as a way to understand the calculation.


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    #9
    4068ac1elhodqr
    Closed Accounts Posts: 9,586 ✭✭✭4068ac1elhodqr


    KBD85 wrote: »
    That's not the correct probability though. The bookie has an edge or overround factored into those odds.

    I'm using this example as a way to understand the calculation.

    Think this has already been anwsered as above:

    True odds: 71/1
    Bookie odds: 60/1

    I always favour these 'hotpicks' type of thing over regular shop tickets, as you have a better return for anything (sub-jackpots) and (optional) lower cost.

    Best bookie prices for 6ball Ire lotto:

    1 ............ 6/1
    2 ............ 60/1
    3 ............ 700/1
    4 ............ 8500/1
    5 ............ 150000/1

    Also have a stronger preference for 5balls hotpick but using Euromillions, (only available bia select markets). This offers a guaranteed prize of 1m and no stars are required for 1.50 cost.

    Yes odds are about 2m/1, but where else can you get the OTE of 1m? For just 5balls 1-50. Note if you get 5balls in regular ticket, you won't ever get anything near 1m.

    Not worth doing the actual shop EM (with the intention of scoring the jacktop), as actual odds are skyhigh at 132m/1 for the 7balls (5+2stars).


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