# "independence of more than two events" notation in the book of Ross

In the book "Introduction to Probability Models" the author Ross explains the independence on two events, and then extends it to more than two events. I think understand the idea, e.g. all possible combinations of the events must hold the equation below to say they are mutually independent. What I do not understand is the usage of apostrophes. Why is he using apostrophes in the paragraph below?

The definition of independence can be extended to more than two events. The events $E_1, E_2,...,E_n$ are said to be independent if for every subset $E_{1'},E_{2'},E_{3'},...,E_{r'}$, $r\leq n$, of these events

$P(E_{1'}E_{2'}E_{3'}...E_{r'})=P(E_{1'})P(E_{2'})...P(E_{r'})$.

In other words, what is the difference between $E_1$ and $E_{1'}$?

If you can provide a small example it would be very nice.

Thanks a lot.

• That's a funny notation..but all it means is that $E_{1'}$ is the first element of the subset in question. The subset might be $\{E_3,E_5\}$ say...in which case $E_{1'}=E_3$ and $E_{2'}=E_5$.
– lulu
Commented Feb 20, 2016 at 18:59
• Oh. I see. Thanks a lot. Commented Feb 20, 2016 at 19:12

As pointed out in a comment, the notation is unusual. A more usual way to write this would be $E_{k_1},\ldots,E_{k_r}$ (with all $k_i$ different).