How do I find the probability?
Three strokes were typed on a keyboard. If all characters typed were letters of the alphabet, what is the probability that the characters typed were three consecutive letters in alphabetical order?
Three strokes were typed on a keyboard. If all characters typed were letters of the alphabet, what is the probability that the characters typed were three consecutive letters in alphabetical order?
1 Answer
If Y, Z, A and Z, A, B are allowed,
If not,
Explanation:
The question is whether the typing of Y, Z, A and Z, A, B counts as three consecutive strokes in alphabetical order count as being ok.
If yes
For the first stroke, it can be anything. For the sake of the calculation, let's say it's A.
For the second stroke, it has to be B to fit with the problem. There are 26 letters in the alphabet but only 1 is "correct" and so the probability of typing it is
For the third stroke, we have to type C, which is again the only letter out of 26 that can be typed to have the condition met, so that's
All told, we have
If no
However, if Y, Z, A and Z, A, B are not allowed, we have another limitation to work with.
For the first letter, we can have any letter between A and X (Y and Z are disallowed), which gives:
We then look at what follows and for each case A through X, we need the specific following letter (so X needs Y, for instance) for both the second and third strokes, which gives what we found before:
giving:
