Comparing UK National Lottery Odds To Hours In A Lifetime.
I was explaining to a not very mathematically minded friend the other day the tremendous unlikelihood of winning the British National Lottery. It occurred to me afterwards that a good way of explaining this would be to equate the odds of winning to the number of hours in a lifetime.
This is what I came up with, there are a couple of questions towards the bottom concerning a bit of help I need finishing it off - it's many years since my Computer Science degree and we only touched on probability at degree level, so I'm a bit rusty.
UK Life Expectancy:
Mean Avg.: 79.1
Days: 365.25 * 79.1 = 28,891.275
Hours: 28,891.275 * 24 = 693,390.6
Odds of winning British National Lottery:
To win the main jackpot 6 unique numbers in the range 1..49 must be chosen. 6 numbers and a bonus number are drawn by the lottery organizers. A bonus number is also chosen by players but this is used only for lower value wins and is irrelevant to the main jackpot. [Note: The bonus number is chosen after the main jackpot numbers and so does not interfere with the 6 main jackpot numbers drawn.]
Odds of choosing all 6 jackpot numbers in the order drawn:
49 * 48 * 47 * 46 * 45 * 44 = 10,068,347,520 to 1
Possible orders of the 6 drawn numbers:
6 * 5 * 4 * 3 * 2 * 1 = 720
Odds of choosing the 6 jackpot numbers in any order and so winning the main jackpot:
10,068,347,520 / 720 = 13,983,816 to 1
(Correct - as advertised on the National Lottery website).
To have a 50/50 chance of winning the main jackpot, play this
13,983,816 / 2 = 6,991,908
Is that right?
The average British person currently lives for 693,390.6 hours, so in ten average British lifetimes you live for this number of hours:
693,390.6 * 10 = 6,933,906
6,933,906 approx. equal to 6,991,908
In words: To give yourself an approx. 50/50 chance of winning the main jackpot of the British National Lottery you would need to play the lottery every single hour of your life for 10 lifetimes. Is that right?
If you were to play the lottery the same number of times as there are possible number choices, 13,983,816, it would take you 20.167 lifetimes of playing every hour.
13,983,816 / 693,390.6 = 20.167 lifetimes
Plainly if you played the lottery every hour of your life for 20.167 lifetimes you would not have a 1.0 probability of winning, but presumably your odds of winning would be quite high. I have no idea how to calculate what the probability of winning would be if you did this. Maybe someone could explain how this is calculated to me please.