The Chances Episode 4: Of getting two similar letters and more!

So, the people succeed the first room (Last episode) and find themselves in a room (still separate from each other) with 130 boxes with each of the 26 letters (no 27th letter/&) and each letter is in 5 boxes. They are scrambled across the rooms. If you get the same letter, the next gate will open, and if you don’t, you get to go back to the first stage.

Here are the chances.

There are 130^2 combinations, or 16900 of them. So that’s our denominator for our chance.

Right now:   x/16900 (x could be anything)

Next, there are 5 of each letter. There should be 25 of each combinations of same letters, so, 25 x 26 is 650. So we have our numerator for the next piece.

Now: 650/16900

We’ll divide 650 by 16900 to see our decimal.

This goes on but this is rounded to the nearest 6th decimal digit:

0.038462

Multiply by 100 to make it into a percentage and:

3.8462%

This has means that there is a very low chance of going on to the third stage, but If you calculate what the odds of getting to the third stage, that would be:

0.01 x 0.038462

Equals:   0.00038462

Even if you make it a percentage by multiplying by 100, it can’t even reach one percent.

It’s 0.038462%, NOT 3.8462%, but 0.038426%. (Man, multiplying by a hundredth and a hundred makes opposite connect, huh?)

Next is a huge pillar, with a lock with 3 numbers (Those numbers you push down and up with your fingers, those kinds). The numbers are from 0 to 9. The two people are in the same room now and need to find the code. They also have to crack the code in sixty attempts, or else, back a stage. However, there is one hint. Someone had the nerve to use a pencil to cross off three numbers in each column. What are the chances of getting the right code?

So, how many combinations are there? We have to eliminate 1 number from each column, so there’s 8 numbers to choose from in each column. So, 8^3 should do it.

It equals 512.

We also already have the other piece of information, which is the 60 attempts part.

So, the odds are now set in fraction form:

60/512 = 0.1171875 = 11.71875%, close to 11.72%.

If we then multiply that with the odds from the second and first gate, we get:

0.00004507265625

Close to 0.00451%!

So, that’s all for today on…

THE CHANCES!

Thanks for reading.

 

 

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The Chances Episode 4: Of getting two similar letters and more!

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