Well it has been a couple of weeks since I last mentioned the word BALLS on this blog, and this is a post about the other kind of balls. A change from the small glass ones that tell the temperature, this set of balls we have all seen, some of us have seen more of these balls than others, but I am not here to pass judgement.
I speak of course (of course they cry) of Tattslotto (major Australian lottery).. As the Australians in the audience will know there was the nine million dollar super draw on Thursday; and no this is not a post to say hey I won, compare your lives to mine and cry. This is a Maths Post.
With a spare 10 mins on an idle Thursday I set my self the task of working out the odds against taking out the "big one" … To win you need to correctly select 5 out of the 5 balls drawn from a pool of 45, and then one ball from one out of the 45 in the Powerball bucket.
Odds on the first ball… 1 chance in 45
Odds on the second….. 1 chance in 44 (one ball less as previous ball removed from draw)
Odds on the third…. 1 chance in 43
Odds on the fourth…. 1 chance in 42
Odds on the fifth…. 1 chance in 41
The odds of drawing all balls (regardless of order) can be found by…
One in forty five * One in forty four * One in forty three * One in forty two * One in forty one
Or 1/ (45*44*43*42*41)
1/ 146,611,080 one chance in one hundred and forty six million (and a bit)…. Still got that lucky feeling. To further stack the odds we still require the "powerball" the odds of drawing the power ball are an additional 1 in 45 chance..
therefore the odds of all five numbers plus the power ball are given by
(1/ (45*44*43*42*41))* (1/45)
Which equals the staggering
One in six billion (and a bit) chance of winning.. The current population estimate 6,552,533,873, if every member of the human race was given a single combination there would still only a 99% chance that someone of the human race would hold the winning combination…
Sometimes I wonder about humanity, is this the hope we have left, a one in 6,597,498,600 that we may be happy and afford every we are told we cant live with out.