Probability 2: Mutually Exclusive &
Independent Events
Pearson: Chapter 10 p358
Homework: Exercise 10.4 Q1, 3,7
Haese & Harris: Chapter 19 p482, 484
Homework: Exercise 19E.1 Q1, 3, 5,6
Exercise 10E.2 Q1 - 4
Mutually Exclusive Events
Mutually exclusive events = events that can’t occur together eg heads and
tails when flipping a coin.
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On a Venn diagram, these
are called disjoint sets
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Example 1. You are given that P(A) = 0.35, P(B) = 0.28 and P(A ∪ B) = 0.62.
Are the events A and B mutually exclusive?
Mutually Exclusive Events
Example 2.
Furcan is an excellent marathon athlete. The probability that he will come in first place in the
school marathon is 0.56. The probability that he comes in second place is 0.38.
a) Calculate the probability that Furcan finishes the marathon in either first or second
place.
b) Calculate the probability that he doesn’t get in either first or second place.
Sample Space Diagrams
Sample Space Grids = when the outcomes are from 2 events, a grid (or
diagram) is an efficient way to show the sample space.
Example 3.
Use a grid to illustrate the sample space for tossing a coin and rolling a die simultaneously. From this
grid determine the probability of:
a) tossing a head
b) getting a tail & a 5
c) getting a tail or a 5
4. Two square spinners, each with 1, 2, 3 and 4 on their edges, are twirled simultaneously. Draw a
grid of the possible outcomes.
Use your grid to determine the probability of getting:
a) a 3 with each spinner
b) a 3 and a 1
c) an even result for each spinner.
Product Rule for Independent Events
5. A 8-sided dice and a 20-sided dice are tossed together.
Determine the probability of getting two 5’s. (without using a grid)
Product Rule for Independent Events
6.
We have two sets A and B. We are given that P(A) = 0.44,
P(A ∪ B) = 0.58.
a) Find P(A ∩ B)
b) Are A and B independent? Give a reason.
c) Are A and B mutually exclusive? Give a reason.
P(B) = 0.25 and
Product Rule for Independent Events
7. Events A and B have probabilities P(A) = 0.4, P (B) = 0.65, and P(A∪B) = 0.85.
(a) Calculate P(A∩B).
(b) State with a reason whether events A and B are independent.
(c) State with a reason whether events A and B are mutually exclusive.
Product Rule for Independent Events
8. There are 3 yellow, 4 blue and 2 red marbles in a bag. Joe randomly took out a
marble, looked at it, and returned it to the bag. He repeated this two more times.
(a) What is the probability he got 3 blue marbles?
(b) What is the probability he got one marble of each colour?
(c) What is the probability he got 2 red and 1 yellow marble?