I can find probabilities of compound events. 9.4 Compound Probability

Compound Events Involves two or more things happening at once. Uses the words “and” & “or”

Using the Word “And” Used to find the probability of two independent events both occurring P(A and B) = P(A) ∙ P(B) Also used for the word “then”

With Replacement P(A then B) means both occur back to back Ex: Drawing an ace then a 4 P(Ace then 4) = P(Ace) ∙ P(4) P(Ace) = 4 52 = 1 13 The ace is then replaced so there are still a total 52 possible outcomes. P(4) = 4 52 = 1 13 4 52 ∙ 4 52 = 1 13 ∙ 1 13 = 1 169 Because the card is replaced, the events are independent and one event does not affect the other.

Without Replacement Let’s look at the same example, but this time we will not replace the ace. P(ace then 4) = P(ace) ∙ P(4) P(ace) = 4 52 = 1 13 Ace is not replaced so now there are only 51 possible outcomes P(4) = 4 51 1 13 ∙ 4 51 = 4 663 Because the card is not replaced, the events are dependent. The event before affects the second event.

Practice 4 15 ∙ 1 5 4 75 What if the first tile is not replaced? 4 15 ∙ 3 14 = 2 35

Using the Word “Or” P(A or B) = P(A) + P(B) Shows the probability of one event or the other occurring when the events have no outcomes in common. Mutually exclusive When events are overlapping and have events in common use the following: P(A or B) = P(A) + P(B) – P(A and B) This prevents us from counting the same probability twice.

Examples Probability of spinning a 2 or 5 Mutually exclusive or overlapping? Both cannot occur at the same time Probability of spinning a multiple of 2 or 5 Some numbers are both multiples of 2 and 5

Assignment Odds p.329 #5-31