# #1 If you stacked up all these lottery tickets, how tall would this stack be?

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?

Solution

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.

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