At the mere mention of probability on the GRE students’ eyes glaze over and all conversation stops, save perhaps for the hushed admission that they don’t like probability.

While probability can be very difficult—and many of the publishers give it short shrift (so there are a lack of practice problems)—keeping a few concepts in mind will make this tricky concept seem somewhat less daunting.

First off we need to know the difference between dependent and independent probability. Today, let’s focus on independent probability.

INDEPENDENT PROBABILITY

If two events have nothing to do with each other then they are independent (makes sense.) For instance, if I toss a fair-sided coin (on average it will come out heads 50% of the time) twice, then the result of one toss does not affect the other toss. So if I get heads on the first toss, then there is still a 50% chance that I will get heads on the next toss.

To illustrate how this concept isn’t always treated rationally, imagine that you have tossed 8 heads in a row. What is the probability that you will toss heads on the 9^{th} toss? It seems very unlikely that you will toss yet another heads. But again, the 9^{th} toss has nothing to do with what happened on the first eight tosses—the chance of tossing a heads is still 50%. Still, most of us would gamble against heads happening again.

To find the probability of a series independent events happening, we find the probability of each event happening and then multiply those probabilities together.

So let’s go back to our streak of 8 heads in a row. To toss this we will have to multiply the probability of getting heads on one toss (50%) eight times. Let’s convert 50% to ½, for ease of calculation. We get (1/2)^8 =1/256 (not a very likely scenario.)

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I always thought what was missing from many probability introductions is the fact that independent means inclusive and exclusive means dependent. Whenever I think about this fact I initially get confused again, until it slowly comes back to memory.

Independent means that other events can either happen or not happen. On the other hand, mutually exclusive means that events are dependent, so force other events to happen or preclude other events from happening.

Maybe you could add this right at the top of the explanation, where I feel it belongs.

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Hi Chris,

I always thought what was missing from many probability introductions is the fact that independent means inclusive and exclusive means dependent. Whenever I think about this fact I initially get confused again, until it slowly comes back to memory.

Independent means that other events can either happen or not happen. On the other hand, mutually exclusive means that events are dependent, so force other events to happen or preclude other events from happening.

Maybe you could add this right at the top of the explanation, where I feel it belongs.