SECTION 7.3MUTUALLY EXCLUSIVE EVENTS
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MUTUALLY EXCLUSIVE EVENTS:
Two events that can not occur at the same time aremutually exclusive
Two events that don’t have any common outcomes
Mutually Exclusive
Not mutually exclusive
because they have somecommon outcomes
They don’t have any common outcomes
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EX: INDICATE WHICH OF THE FOLLOWING EVENTS AREMUTUALLY EXCLUSIVE
i) A dice is rolled
A) an even number is rolled
C) a “5” is rolled
B) an odd number is rolled
D) a number less than 3 is rolled
ii) A card is selected from a deck
A) Card is a club
C) Card is red
B) A Face card is chosen
D) A spade is chosen
Events A and B are Mutually Exclusive
Events A and C are Mutually Exclusive
Events C and D are M.E.
Events A and C are Mutually Exclusive
E) An ace is chosen
Events A and D are Mutually Exclusive
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Events C and D are M.E.
Events B and E are M.E.
NON-MUTUALLY EXCLUSIVE EVENTS
If two events are not mutually exclusive then:
The area of both circles combined is equal to:
Area of the red circle plus the area of the blue circle
subtract the common area in between
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Cancel each other out
Group the pieces back togetherand the areas will be equal
Ex: A card is chosen, what is the probability that the card isa spade or a royal card?
Practice: what is the probability that the card is less than 8or a heart? (Ace is included)
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ASSUME THAT ALL STUDENTS MUST TAKE MATH &SCIENCE. THE PROBABILITY OF PASSING A MATH TEST IS70% AND THE PROBABILITY OF PASSING A SCIENCE TEST IS80%. THE PROBABILITY OF PASSING BOTH TEST IS 65%.FIND THE PROBABILITY OF EACH EVENT:
a) Student passes math but not science
b) Student does not pass both test
c) Student passes Math or Science
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EX: THE RESULTS FROM A MARATHON IS RECORDED. 35%OF THE RUNNERS TOOK MORE THAN 3 HOURS, 40% LESSTHAN 2 HOURS, AND 10% FINISHED WITHIN 1 HOUR. FINDTHE PROBABILITY OF THE FOLLOWING:
i) A runner takes betweenone and two hours
ii) A runner takes betweentwo and three hours
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