I'll give 5 examples

  1. Getting a sum of 10 in a toss of 2 dice

  2. Getting a hand of 8 cards consisting of 3 aces and 5 face cards

  3. Seating 7 persons in a row, 2 of whom should sit together

  4. Getting at least 2 heads in a toss of 4 coins

  5. Getting 2 red balls from a box containing 5 red balls and 6 blue balls

I believe 1, 3, and 5 are simple events, while 2 and 4 are compound events

But my problem is that I cannot tell if this is true or not, I'm uncertain of whether an event is simple or compound. How can I tell the difference?

  • 4
    $\begingroup$ How do you define "simple event" and "compound event." I personally have never bothered making a distinction as theoretically any event can be expressed as a single set without the need of using multiple sets to do so (even if it may be made more convenient in doing so). $\endgroup$ – JMoravitz Mar 11 '17 at 8:40
  • $\begingroup$ I believe that's my main problem as well, I can't define the meaning of simple or compound, yet I see it in my text book and no explanation is given. I guess this question is subjective in some way. Sorry about that. $\endgroup$ – Jan Gamma Mar 11 '17 at 8:42
  • 2
    $\begingroup$ Even using a more standard term such as "atomic event" (an event which is a singleton set, containing only a single outcome), this is subjective since we are told nothing of the sample space. A common sample space for rolling two dice is $\{(1,1),(1,2),(1,3),\dots,(2,1),(2,2),\dots,(6,6)\}$ but equally valid sample spaces are $\{2,3,4,\dots,12\}$ and $\{even,odd\}$ as well as $\{10,\text{not}~10\}$ $\endgroup$ – JMoravitz Mar 11 '17 at 8:45
  • $\begingroup$ At first glance I would distinguish Q4 as needing addition (or subtraction) while I suspect the other questions can be done just by multiplication and division. But then I start wondering about Q1: is it $\frac{2+1}{6^2}$?. $\endgroup$ – Henry Mar 11 '17 at 10:05
  • $\begingroup$ here's a great resource for intuitively understanding compound probability with the aid of visualizations. students.brown.edu/seeing-theory $\endgroup$ – Daniel Xiang Mar 11 '17 at 16:20

I looked up the definition of compound event and found my original comment was wrong, but I think I can explain compound event now:

Simply stated, a simple event can happen only one way (has only one simple outcome) whereas a compound event can happen multiple ways (it's a subset of the sample space consisting of more than one simple outcome).

An easy example: The experiment is roll a single die. The sample space (set of all possible simple outcomes) is {1,2,3,4,5,6}. The event '$E$=getting a number more than two and less than four' is a simple outcome, as it can only happen if you get 3 on the die, $E$={3}. However, the event '$F$=getting an even number' is a compound event, because if you get 2, 4 or 6 then the event happens, $F$={2,4,6}.

From this definition, you can show that all of your above example are compound events.

Event 1 = {(4,6),(5,5),(6,4)} three simple outcomes so compound.

Event 2 has $\binom 4 3*\binom {12} 5$ simple outcomes, one of which is aces of diamonds, hearts and clubs, all the jacks, and king of hearts. (I'm assuming this is choosing 8 cards from a standard deck without replacement.)


Edit: By the way, things do get a bit messy. Let me give an example. Another possible sample space for rolling a die is {even,odd}. It is not useful for finding the probability of rolling a number less than 2, but it works if we want to know the probability of getting an even number. So is the event getting an even number really compound? Shrug.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.