probability problem

[MdAbuAsad]

in probability problem, how will I understand the two events are mutually exclusive, independent or dependent ? Could you please clarify it with some example ?
Thanks.

[jnelson0612]

in probability problem, how will I understand the two events are mutually exclusive, independent or dependent ? Could you please clarify it with some example ?
Thanks.

Well, let's say that for instance you are going to choose a three digit code for a lock. You can choose the numbers 0-9 for each digit.

Events are independent if they have no impact on or relationship with each other. For instance, if I can choose any digit for any of the three numbers, and I can have repeats, then I have 10 possibilities for the first digit, 10 possibilities for the second digit, and 10 possibilities for the third digit, or 10 * 10 * 10 = 1000 possibilities.

Events are dependent if one event influences another. For instance, you might find that you have the constraint that you cannot have repeating digits. In this case, if you choose a 4 for the first digit, you cannot use 4 again, and you only have nine possibilities for the second digit. Let's say that you choose 7. Now you can't use either 4 or 7 for the third digit, so you have eight possibilities. Thus, the number of outcomes is 10 * 9 * 8 = 720 possible combinations.

I hope that this helps.

[RonPurewal]

in probability problem, how will I understand the two events are mutually exclusive, independent or dependent ? Could you please clarify it with some example ?
Thanks.

^^ i've never seen a problem on which the notion of independence mattered.

on the gmat, you should be able to address the probabilities of consecutive events by multiplying them—regardless of whether the two events are actually "independent".

e.g., there are 13 spades in a standard deck of 52 cards.
• if you pick a card, put it back, and then pick another card, the probability that you'll get spades both times is 13/52 x 13/52.
• if you pick a card, don't put it back, and then pick another card, the probability that you'll get spades both times is 13/52 x 12/51.
note that you can just multiply the probabilities in both cases; there's no need to think explicitly about the notion of "independence", which will just needlessly complicate things.

[MdAbuAsad]

Thanks Nelson and Ron.
Ron, I've already got it from "Thursdays with Ron"--Study Hall: February 17, 2011.

[RonPurewal]

excellent.

[Humstudents]

So informative and amazing.

[jnelson0612]

Good to hear.

[RonPurewal]

thanks