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MUTUALLY EXCLUSIVE INVESTIGATION
Mutually Exclusive is when two events CANNOT occur at the same time.
1. A die is rolled and you are trying to find the probability of certain events.
a. List all the possible outcomes when rolling a die.
b. What is the probability you roll an odd number?
P(odd) =
c. What is the probability you roll a 4?
P(4)=
d. What is the probability you roll an odd or a 4?
P(odd or 4)=
Notice that the probability of rolling an odd or a 4 is just the probability of rolling an odd plus the probability
of rolling a 4. You can add the two probabilities because they do not share the same outcomes. The
outcome for the event of rolling a 4 is just 4, and the outcomes of the event of rolling an odd is 1,3,and 5.
They are mutually exclusive. There is no overlapping number.
P(odd or 4) = P(odd) + P(4)
4/6 =
3/6 + 1/6 = 4/6
You can also think of this with a Venn Diagram where there is a circle with odd numbers and a
circle for 4 and there is no shared value where the circles overlap.
odd #’s
1,3,5
4
2. A die is rolled and you are trying to find the probability of certain events.
a. What is the probability you roll an even number?
P(even)=
b. What is the probability you roll a number less than 3?
P( <3)=
c. What is the probability you roll an even or a number less than 3?
P(even or <3)=
Notice that the probability of rolling an even or a number less than 3 is NOT equal to the probability of
rolling an even plus the probability of rolling a number less than 3. You CANNOT add the two probabilities
because they share an outcome of 2. The outcomes for rolling an even are 2, 4 and 6 and the outcomes for
rolling a number less than 3 are 1 and 2; 2 is an outcome for both events. These are NOT mutually exclusive.
P(even or 2) = P(even) + P(2)
3/6 ≠ 3/6 + 1/6 = 4/6
You can also think of this with a Venn Diagram, where there is a circle with even numbers (2,4,6)
and a circle for numbers less than 3 (1,2) and there IS an overlap value, 2.
#’s less than 3
1
3. You draw a card from a deck of cards. (A deck of cards has 13 red hearts, 13 red diamonds, 13 black
spades, and 13 black clubs.)
a. What is the probability you draw a Jack?
b. What is the probability you draw a card with a number less than 5?
c. What is the probability you draw a jack or a number less than 5?
d. Does the probability of a jack and the probability of a number less than 5 add up to the probability of a jack
or a number less than 5? Show proof.
e. Are the two events, probability of a jack and the probability of a number less than 5, mutually exclusive?
Why or why not?
4. You draw a card from a deck of cards. (A deck of cards has 13 red hearts, 13 red diamonds, 13 black
spades, and 13 black clubs.)
a. What is the probability you draw a spade?
b.
What is the probability you draw an even card?
c. What is the probability you draw a spade or an even card?
d. Does the probability of a spade and the probability of an even add up to the probability of a spade or an
even? Show proof.
e. Are the two events, probability of a spade and the probability of an even, mutually exclusive? Why or why
not?