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
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
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
"A" can be in any of 7 positions around the table.
Whichever position it is in, B has a $\displaystyle \frac{4}{6}$ 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 $\displaystyle \frac{2}{3}$ wherever "A" happens to be.