Street Lights
Suppose you're driving and that there are 10 traffic lights (sorry I meant to say traffic lights) you have to get through. Assuming that there's no traffic, what is more likely?
A) Run into 5 red lights and 5 green lights.
B) Run into a red light and a green light, in no particular order, for each two that you pass.
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1 solution
We can think of running into red/green lights with 0's and 1's. In this case, we may write run into red ↔ 1 and run into green ↔ 0 . For example, for the first two that we pass, suppose we run into a red light first and then a green light. Then this can be expressed as 10. If it was the other way around, we may represent it as 01. Then situation B) can be represented by a sequence of 0's and 1's that fill in the blanks in the picture below:
| _ | _ | _ | _ |__ |
For example, if we got red, green, green, red, green, red, red, green, red, green, then we may represented with the sequence below.
|10|01|01|10|10|
Now, notice that any sequence for B) is also a sequence for A); that is, the picture above represents an outcome for A). But in A) we can have more sequences like red,red, green, red, green, green, red, green, red and green.
|11|01|00|10|10|
Since the set of all outcomes for B) is a subset of the set of all outcomes for A), then A) is more likely.