P - What's the Probability? Lesson

What's the Probability?

Let's try a problem. Go back to the license plates - a GA license plate has 3 letters and 4 numbers. Recall that there are 175,760,000 different license plates that could be made. Well, what if we wanted to know the probability that the license plate contains only the letters A, M or D and all even numbers. We can determine how many ways that can happen: $3\cdot3\cdot3\cdot5\cdot5\cdot5\cdot5=16,785$

So, there are 16,875 license plates that would have only A, M or D and all even numbers. So, the probability of that happening is:

$P\left(E\right)=\frac{16785}{175760000}\approx0.00009$

If two events are independent , then the probability of those two things happening is found by multiplying the probabilities together. Events are considered independent when the outcome of one, does not affect the outcome of the other.

Let's take, for instance, flipping a coin. Each flip is independent of the outcome prior. So the probability of getting heads on the first flip is Ѕ and the probability of getting heads on the second flip is still Ѕ - this means the probability of getting heads, then heads again is:

$P\left(HandH\right)=\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}=0.25$

So, what happens if two events are dependent?

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