Lottery Odds

[fireflybob]

Anyone out there know how to calculate these?

On the Thunderball you pick 5 numbers between 1 and 39 and also 1 number (the thunderball) between 1 and 14.

The odds of winning the jackpot (£500,000) are 1 in 8,060,598.

If you do a syndicated entry which covers all the thunderballs (ie 14 entries covering each thunderball from 1 to 14) then what are the odds of winning the jackpot (assume choice of the 5 numbers is the same throughout).

Thanks for any help

[Diver_Dave]

FFB....

Try here,

Excellent background to the whole gaming probability calculations
Taking Chances: Winning with Probability: Amazon.co.uk: John Haigh: Books

Additionally, this one's fun!

Conned Again Watson: Cautionary Tales of Logic, Math and Probability: Amazon.co.uk: Colin Bruce: Books


Enjoy

Regards
DaveA

[fireflybob]

DD, thanks!

[Torque Tonight]

1 in 575,575. 14 times greater than the original odds because all 14 possibilities for the last number have been covered. One entry will definitely have the correct thunderball.

Original probability is:

(5/39)*(4/38)*(3/37)*(2/36)*(1/35)*(1/14)=(1/8060598)

where the first 5 brackets refer to picking 5 numbers out of a set of 39 where the order in which they are picked does not matter. The sixth term is picking one number out of an independant set of 14 (the thunderball). This is the term that drops out if you cover all 14 thunderball possibilities:

(5/39)*(4/38)*(3/37)*(2/36)*(1/35)=(1/575757)