Probability

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Independent and Dependent Events

Two events are independent if one event happening doesn't affect the probability of the other happening. For example, picking a blue ball, replacing it, then picking a red ball.

Two events are dependent if one event happening does affect the probability of the other happening. For example, picking a blue ball and then picking a d ball without replacing the blue ball first.

Independent Events

P(A and B) = P(A) x P(B)

P(A or B) = P(A) + P(B) - P(A and B)

When events can't happen together they're called MUTUALLY EXCLUSIVE.

Conditional Probabilities

This is the probability of A given B. In other words, the probability of A happening given that B happens.

A given B = A|B

If events A and B are independent, then (A given B) = P(A) and P(B given A) = P(B)

If events A and B are dependent, then P(A and B) = P(A) x P(B given A)