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  • Exclusive events and intersecting events
  • Conditional Probability

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  1. Statistics

Probability

PreviousMeasuring Central TendencyNextStandard Deviation , Variance

Last updated 5 years ago

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Exclusive events and intersecting events

Take this as a table

These two events are mutually exclusive because it’s impossible for the ball to land in a pocket that’s both black and red.

What about the black and even events? This time the events aren’t mutually exclusive. It’s possible that the ball could land in a pocket that’s both black and even. The two events intersect

Conditional Probability

. we want to find the probability that the pocket is even, given that we already know it’s black. In other words, we want to find out how many pockets are even out of all the black ones. Out of the 18 black pockets, 10 of them are even, so

So how can we generalize this sort of problem? First of all, we need some more notation to represent conditional probabilities

, which measure the probability of one event occurring relative to another occurring.

We represent conditional probability with P(A | B)

The probability of A give that we know B has happened.

Venn diagrams aren’t always the best way of visualizing conditional probability.

Don’t worry, there’s another sort of diagram you can use—a probability tree.