Warm-up1) You roll a number cube once. Then roll it again. What
is the probability that you get 2 on the first roll and a number greater than 4 on the second roll?
2) You toss a coin 3 times. What is the probability you get 3 tails?
3) You have 7 cards. Each card has a letter on it spelling out the word ALGEBRA. Without replacing a card, what is the probability of selecting:
a) A, then G b) E, then A, then R
Independent. P(2)=1/6 P(greater than 4)= 2/6 P(2,then greater than 4) = 1/18
Independent. P(T,T,T) = ½ x ½ x ½ = 1/8
Dependant. P(A, then G) = 2/7 x 1/6 = 1/21
Dependant. P(E,then A, then R)= 1/7 x 2/6 x 1/5 =1/105
State if the events are independent or dependant and find each probability.
14.8a Compound Events
• The probability of two events occurring is called a ________________. Independent and dependent events are compound events.
Two other types of events are also compound events…________________,
and ______________________.
Compound Events
Mutually Exclusive
Overlapping Events
Mutually exclusive means they can not happen at the same time!Overlapping means they can happen at the same time! (You have to take out the duplicates)
Review…..
• Two events are INDEPENDENT if the occurrence of one event does not affect the occurrence of the other! (Replacement might be a hint)
• Two events are DEPENDENT if the occurrence of one event does affect the occurrence of the other. (Non-replacement)
Disjoint or Mutually exclusive Events!
Two event are mutually exclusive if they have no outcomes in common.
…….. ….
Key Concept: If A and B are mutually exclusive events, then the probability of A or B is: P(A or B)= P(A) +P(B)
Look for the word “ or “ It means addition
Mutually Exclusive
Ex. 1 A card is randomly selected from a standard deck of 52 cards. What is the probability that it is a 10 or a face card?
Disjoint event
Event A= 10
Event B= Face Card
P(A or B) = P(A) + P(B)
P(A or B) = 4 12 16 452 52 52 13
Overlapping or Inclusive Event
Ex. 2 A card is randomly selected from a standard deck of 52 cards. What is the probability that it is a face card or a spade?
Event A=Face Card
Event B= Spade
As you can see from the Venn Diagram, being a spade and a face card at the same time is possible.
P(A or B) = P(A)+P(B)-P(A and B)12 13 3 22 1152 52 52 52 26
Your turn to practice• Ex. 3 What is the probability of rolling a standard six-sided
number cube and getting a 3 or a 5.
• Ex. 4 You roll a number cube. What is the probability that you get an odd number or a number greater than 3?
Solution: find the probability of the events. Let event A be getting an odd number and let Event B be getting number greater than 3.
P(A)=3/6 P(B)= 3/6 P(A and B) = 1/6
P(A or B) = 3/6 + 3/6 – 1/6 = 5/6 0.83
P(3) = 1/6 P(5)= 1/6
P(3 or 5)= 1/6 + 1/6 = 1/3
Summary
Name two examples of compound events and if they would be independent, dependant, mutually exclusive, or overlapping?
Homework time
• Worksheet 14.8 ALL….make sure you have the right type of compound event: Is it Independent? Dependent? Mutually Exclusive? Overlapping?
• IT makes a difference: the word and means: Multiply. The word or means add
