# 12 4 Probability of disjoint and overlapping events

12. 4 Probability of disjoint and overlapping events. Geometry EQ: How do you find the probability of compound events?

Compound events UNION: When you consider all the outcomes for either of two events A and B, you form the union of A and B There is one or more outcomes in common (overlapping) 10 January 2022 Geometry 12. 4 Compound events Disjoint and overlapping. 2

Compound events Intersection : If you only consider the outcomes shared by both A and B, you form an intersection of A and B Be careful to not over count the intersection twice in an intersection. 10 January 2022 Geometry 12. 4 Compound events Disjoint and overlapping. 3

Compound events Disjoint, mutually exclusive : If the two events are have no outcomes in common, then the two events are considered disjoint or mutually exclusive. A and B share nothing in common. 10 January 2022 Geometry 12. 4 Compound events Disjoint and overlapping. 4

A card is randomly selected from a standard deck of 52 playing cards. What is the probability that it is a face card or a spade? An intersection is formed. The J, Q and K of spades There are 12 outcomes in event A and 13 outcomes in event B. We cannot add the probability of event A to probability of event B because the J, Q, K of spades would be counted twice. P(A and B) must be subtracted. 10 January 2022 Geometry 12. 4 Compound events Disjoint and overlapping. 5

Disjoint mutually exclusive A card is randomly selected from a standard deck of 52 playing cards. What is the probability that it is a 10 or a face card? No intersection formed. A and B are disjoint. 10 January 2022 Geometry 12. 4 Compound events Disjoint and overlapping. 6

60 adults went through the drive thru for breakfast at Mc. Donalds. 54 bought either coffee or orange juice. There were 35 who bought coffee and 45 who bought orange juice. What is the probability that a random customer bought both coffee and Orange juice? 10 January 2022 Geometry 12. 4 Compound events Disjoint and overlapping. 7

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