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Asked: 2026-06-12T04:26:53+00:00

Ok so Im a bit lost on this. So looking at a this 0

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Ok so Im a bit lost on this. So looking at a this 0 0 0 0 and looking at each 0 individually with each one has a probability of 0.01 of turning from a 0 to a 1
Ok so there are 4 numbers each number can be a 0 or a 1

Probability is measured by determining how likely an event is to happen divided by the number of possible outcomes

The possible outcomes are:

0000
0001 0010 0100 1000
1100 1001 1010 0101 0011 0110
1110 0111 1011 1101
1111

So there is a total of 16 possible outcomes or 4^2 i.e. 4 number by the possible outcomes they can be 0 or 1

So the probability of the string of number to be to turn from 0000 to 1111 would be
0.01/16

The probability of the number to be from 0000 to 0100 would also be
0.01/16?

And the probability of all the number to stay the same would i.e 0000 to 0000
would still be 0.01/16

It kinda makes sense but I don’t know would all of them be the same probability?

Or am I doing this wrong
so each number has a 0.01 chance to change so for the string to go from 0000 to 1111 would be 0.01 *4 / 16 or 0.0025

And the chance to change from 0000 to 0100
would be 0.01 * 1 /16

And to change from 0000 to 0000 would be
0.01*0 /16

Thanks for any help with this

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1 Answer

  1. Editorial Team

    There are two things here. One, the number of possible outcomes (16) and the probability of each outcome.

    Since the probability of a single bit being flipped to 1 is skewed towards it being 0, then the distribution of outcome probabilities is not even. If there was a 50% chance of a 1 or a 0 in each spot, then the probability of each of the 16 outcomes would be 1/16. That is not the case here.

    The approach I’d take is to group the numbers into buckets. Of the 16 outcomes, 1 has zero 1’s, 4 have one 1, 6 have two 1’s, 4 have three 1’s, and 1 has four 1’s.

    The probability of four 0’s is 99%^4. The probablity of one 1 is 1% x 99%^3. The probability of 2 is 1%^2 x 99%^2. etc. Calculate each of the probabilities , then divide by the size of the bucket. Add them up, and they should equal 100% (sanity check).

    I checked it in a spreadsheet, and the results seem good:

    Outcome Probability
0000    0.96059601
0001    0.00970299
0010    0.00970299
0100    0.00970299
1000    0.00970299
0011    0.00009801
0101    0.00009801
1001    0.00009801
0110    0.00009801
1010    0.00009801
1100    0.00009801
0111    0.00000099
1011    0.00000099
1101    0.00000099
1110    0.00000099
1111    0.00000001
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