10.2 ~Notes packet from yesterday Have homework out from last night

Tree Diagram A way of organizing the possible outcomes for probability events.

Independent Events Events where the occurrence of one event does not affect the probability of other events.

Dependent Events Events where the occurrence of one event can affect the probability of other events.

Multiplication Rule for Independent Events If 𝑛 1 , 𝑛 2 , 𝑛 3 , and so on, represent independent events, then the probability that this sequence of events will occur can be found by multiplying the probabilities of the events. 𝑃( 𝑛 1 and 𝑛 2 and 𝑛 3 and…) = 𝑃( 𝑛 1 ) 𝑥 𝑃( 𝑛 2 ) 𝑥 𝑃( 𝑛 3 )𝑥…

Conditional Probability The probability of one event (A) given an event (B) has already occurred. Notation: P(A|B) Reading: “Probability of A given B” Example: What is the probability of drawing a spade given you first draw a heart from a standard deck of cards? Assume you do not replace your cards. P(S2|H1) =

Multiplication Rule for Conditional Probability If 𝑛 1 , 𝑛 2 , 𝑛 3 , and so on, represent independent events, then the probability that this sequence of events will occur can be found by multiplying the conditional probabilities of the events. 𝑃 𝑛 1 and 𝑛 2 and 𝑛 3 and… = 𝑃 𝑛 1 𝑥 𝑃 𝑛 2 𝑛 1 𝑥 𝑃 𝑛 3 𝑛 1 and 𝑛 2 𝑥…

Example Mr. Roark teaches three classes. Each class has 20 students. His first class has 12 sophomores, his second class has 8 sophomores, and his third class has 10 sophomores. If he randomly chooses one student from each class to participate in a competition, what is the probability that he will select three sophomores? A. Find the probability a sophomore is selected for each class.