Many years ago we were in The Jolly Quizmaster and overheard a man criticising his wife: "I can't believe how stupid she's been. She has picked six odd numbers on the Lottery - I mean what are the chances of six odd numbers coming up? It must be astronomical, so that's a pound wasted". His colleagues nodded and sympathised with the man for having such an intellectually-challenged wife.
We on the other hand exchanged knowing grins, recognising the irony of the man's pronouncement.
Of course every set of six numbers has exactly the same probability of winning; six odd numbers, six even numbers, the number one, two, three, four, five and six, even last week's winning numbers.
However, this et us thinking - what is the probability of six odd numbers being drawn, and come to that, what is the probability of six even numbers being drawn?
You might realise from the entry fee that this was some time ago when there were only 49 numbers rather than 59 numbers, as now.
So what are the four probabilities; odd and even, with 49 and 59 numbers?
Taking the 49-number case with odd numbers the probability of the first being odd is 25/49, and the second number being odd is 24/48 and so on giving
25 x 24 x 23 x 22 x 21 x 20 / 49 x 48 x 47 x 46 x 45 x 44 which is 0.0126 or 1.26%, or about one in 79 - once in just over 18 months.
Even numbers are slightly different, as there are only 24 so the sum is
24 x 23 x 22 x 21 x 20 x 19 / 49 x 48 x 47 x 46 x 45 x 44 which is 0.0096 or 0.96%, or about one in 104 - once in just under two years.
The sums are similar for the 59-number case:
All six odd numbers is 0.0132 or 1.32%, or about one in 76 - once in just under 18 months.
All six even numbers is 0.0105 or 1.05%, or about one in 95 - once in just under two years.