Question

the first 12 alphabets are written down at random. what is the probability that A and B are written down side by side
a. 1/5
b. ¼
c. 1/6
d. 1/8

Answer 1

I would do it like this.
There are 2 different options:
a, A or B is the first or last in the list
b, A or B is somewhere in the middle.

a, It is 2/12=1/6 chance that lets say A is the first or the last.
Than there is only 1 way way that they can be next to each other. So the chance is 1/11

b, It is 10/12=5/6 chance that lets say A is not the first/last.
Than there are two ways they can be next to each other (in front/behind). So the chance is 2/11.

we have to add these.
1/6*1/11+5/6*2/11=11/66=1/6

Answer 2

Do those account for B being first or last in part a (and conversely not first/last in b)?

Answer 3

I dont get you, sorry.

Answer 4

I just thought of placing them 1 by 1. So first I only cared about the position of A than counted the chance that B is next to it.

Answer 5

Probability is my favourite maths subject! You have to think a lot, and it is just pure logic

Answer 6

thank u :)

Answer 7

In pasrt a) of your solution you mention that there is a 1/6 chance of A being in the first or last position. But it's possible that you have "BA__________" or "__________AB" which I'm not sure is covered in your case.

I love probability too...but I've been out of it for enough years that I'm losing my edge. You might be right...I might just not be seeing it.

Answer 8

Oh I get you, but I dont think that this matters here. (I am 98% confident :-))

Answer 9

It might not...looking at it more, part B covers the cases where A is *not* first/last...which would include my example. You then place B on either side...which might include it being in the first or last position (depending on A being #2 or #11).

Ok..I can conceed :) Good solution!