# Thread: I really need help for this probability question :(

1. ## I really need help for this probability question :(

The letters A, B, C, D, E, F, G are arranged around a circle. Find the probability that A and B are not together.

It's a probability homework question, and i'm really struggling to get my head around this kind of probability

2. ignore the circle and consider the 3 points around A.

i will use "x" to denote an unknown letter.

The total number of arrangements of xAx = 6 * 1 * 5 = 30

You want to exclude the cases where B is on the left of A
BAx = 1 * 1 * 5 = 5

And the cases where B is on the right of A
xAB = 5 * 1 * 1 = 5

So, there are 10 arrangements where A and B are together.

Probability = 1 - 10/30 = 2/3

Warning my answers on these types of questions tend to be very unreliable

3. Originally Posted by phillychum
The letters A, B, C, D, E, F, G are arranged around a circle. Find the probability that A and B are not together.

It's a probability homework question, and i'm really struggling to get my head around this kind of probability
Another approach is to count the number of ways that A and B are together by considering the arrangements of AB, C, D, E, F, G (5!) and BA, C, D, E, F, G (5!). Divide this by the number of arrangements of A, B, C, D, E, F, G (6!) and subtract the result from 1.

4. Originally Posted by phillychum
The letters A, B, C, D, E, F, G are arranged around a circle. Find the probability that A and B are not together.

It's a probability homework question, and i'm really struggling to get my head around this kind of probability
"A" can be in any of 7 positions around the table.

Whichever position it is in, B has a $\frac{4}{6}$ chance of not being next to "A", as there are 4 of the remaining 6 positions not adjacent to "A".

The probability of "A" not being next to "B" is $\frac{2}{3}$ wherever "A" happens to be.