Another way to look at the odds on the California Lottery
(Inspired by a parenthetical comment by William Gibson in one of his books.)
The current California Mega Millions lottery game has you pick 5 numbers, 1 through 56, and a final bonus number, 1 though 46. You win the millions if you match all 6. The 5 numbers can't be equal to each other.
This means the odds are 1 in 56*55*54*53*52*46/(5*4*3*2). This is 1 in 175,711,536.
Another way to look at this is that you're implicitly picking one number between 1 and 175,711,536. It just happens to be called something weird (namely, the concatenation of your 6 numbers).
It takes a 28-bit integer to hold any number between 1 and 175,711,536. (27 bits and change, really). Thus, you're trying to match your 28-bit number with a 28-bit number the state picked.
A 28-bit integer is just a series of ones and zeros.
You can also represent ones and zeroes as coin flips - heads or tails.
So basically what you're doing by playing the California lottery is, trying to guess heads or tails correctly 28 times in a row.
Try it - bet you can't get to 10.
The current California Mega Millions lottery game has you pick 5 numbers, 1 through 56, and a final bonus number, 1 though 46. You win the millions if you match all 6. The 5 numbers can't be equal to each other.
This means the odds are 1 in 56*55*54*53*52*46/(5*4*3*2). This is 1 in 175,711,536.
Another way to look at this is that you're implicitly picking one number between 1 and 175,711,536. It just happens to be called something weird (namely, the concatenation of your 6 numbers).
It takes a 28-bit integer to hold any number between 1 and 175,711,536. (27 bits and change, really). Thus, you're trying to match your 28-bit number with a 28-bit number the state picked.
A 28-bit integer is just a series of ones and zeros.
You can also represent ones and zeroes as coin flips - heads or tails.
So basically what you're doing by playing the California lottery is, trying to guess heads or tails correctly 28 times in a row.
Try it - bet you can't get to 10.