11.3 - Independent and Dependent Events

The occurrence of one event does not affect the probability of another

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

A coin is flipped three times. What is the probability it lands heads all three times?

The outcome of any flip does not affect the next one, so the events are independent.

Multiply the probabilities.

 $\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{8}$  

The occurrence of one event affects the probability of the other

If A and B are dependent events, then P(A and B) = P(A) * P(B | A), where P(B | A) is the probability of B, given that A has already occurred.

A standard deck of playing cards has 52 cards made up of 4 suits (diamonds, hearts, clubs, spades) of 13 cards each.

You select a diamond from the deck and do not replace it. What is the probability that you select another diamond with your next draw?

Multiply the probabilities

 $\frac{13}{52}\cdot\frac{12}{51}=\frac{1}{4}\cdot\frac{4}{17}=\frac{1}{17}$