Independent Events

Two probabilistic events $ H_1$ and $ H_2$ are said to be independent if the probability of $ H_1$ and $ H_2$ occurring together equals the product of the probabilities of $ H_1$ and $ H_2$ individually, i.e.,

$\displaystyle \hat{p}(H_1 H_2) = \hat{p}(H_1)(H_2)$ (C.2)

where $ \hat{p}(H_1 H_2)$ denotes the probability of $ H_1$ and $ H_2$ occurring together.


Example: Successive coin tosses are normally independent. Therefore, the probability of getting heads twice in a row is given by

$\displaystyle \hat{p}(H H) = \hat{p}(H)\hat{p}(H) = \frac{1}{2}\cdot\frac{1}{2} = \frac{1}{4}.$ (C.3)


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