Imagine a lottery game where the chances of you winning the game stand at about 1 in 200 million. If you stacked up all these lottery tickets, how tall would this stack be?
Let's break this problem into two parts.
- The total number of tickets
- The thickness of each ticket
Since the chances of you winning the game stand at about 1 in 200 million, that implies that the total number of the different variety of tickets are 2 * 10^8.
Assuming the thickness of this single ticket is..pesky. Let's instead try to assume the thickness of a bundle of tickets and try to find the thickness of a single ticket from there.
Now, let's break this down further into what we know about lottery tickets. A normal lottery ticket is thicker than paper but thinner than a pack of playing cards.
So, the bundle of this lottery ticket resembles more closely a pack of playing cards of about
1 cm than it does a pack of paper.
Thus, a packet of 52 lottery tickets can be assumed to be 1 cm thick.
Or, the thickness of each lottery ticket can be assumed to be about 1 / 52 cm
Or, 0.02 cm / ticket
Or, in scientific notation, this can be written as 2 * 10 ^-2 cm / ticket
Converting this into meters and kilometres, we have
2 * 10^-2-2 meters / ticket
Or, 2 * 10^-4 meter / ticket
Or, the thickness of all the tickets can be
2 * 10^-4 * 2 * 10^8 meters
Or, 4 * 10^4 * 10^-3 kilometres
Or, 40 kilometres.