Download Mutually Exclusive Events (Disjoint Events) Using a Venn Diagram

5.2 – The Basic Rules of Probability
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Recall from last day that:
④ The probability of any event is a number between 0 and 1.
④ All possible outcomes together must have a probability whose sum is 1.
④ The probability of an event and its compliment is equal to 1.
Mutually Exclusive Events (Disjoint Events)
Two events are mutually exclusive or disjoint if they have no outcomes in
common and so can never occur together.
Addition Rule for Mutually Exclusive Events:
If A and B are mutually exclusive, then P(A or B) = P(A) + P(B)
Example of Mutually Exclusive Events:
Using a Venn Diagram to Understand Mutual Exclusivity.
5.2 Questions – Key Probability Concepts
Sample Spaces: Describe the sample space for each situation.
a. A couple has 3 children.
b. Two cards are drawn in succession from a regular 52-card deck. The first card is
replaced after it is drawn.
c. Two cards are drawn in succession from a regular 52-card deck. The first card is
not replaced after it is drawn.
d. A student enrolls in a calculus course and at the end is assigned a letter grade.
e. A test for leukemia can either result in a positive or negative result. The test may
also be correct or incorrect.
The Multiplication Principle/Counting: Count the number of events in each outcome.
a. A couple has 4 children.
b. A coin is tossed 3 times.
c. Two cards are drawn in succession from a deck of 52-card deck (without
replacement). How many ways can you get 2 hearts?
d. A license plate has 3 numbers from 0-9, followed by 3 letters from A-Z.
e. A card is drawn from a deck. How many ways can you get:
a. A red card
b. A queen and a heart
c. A queen or a heart.
The Complement: For each event, describe the complement.
a. P(at least 1 boy in 4 children)
b. P(at least 1 heart in two draws from a deck of 52 cards)
c. P(a 3 or 4 on a roll of two dice)
d. P(a 3 and a 4 on a roll of two dice)
Mutually Exclusive (Disjoint) Events
1. When an M&M is drawn at random from a bag, the following probabilities apply:
P(Brown)=0.3, P(Red)=0.2, P(Yellow)=0.2, P(Green)=0.1, P(Orange)=0.1,
P(Blue)=?
a. Find P(Blue) so that the probability model is legitimate.
b. Find P(not Brown).
c. Find P(Red or Yellow)
d. What if we draw 2 M&Ms in a row (assume we replace the first one before
drawing the second)? Are these events mutually exclusive?
e. Find P(Red and Yellow in two draws with replacement).
2. The US Census asks people to classify themselves according to race. Each person
chooses one or more race from a list. If you choose an American at random, the
following probabilities apply:
Hispanic Not Hispanic
Asian
0.000
0.036
Black
0.003
0.121
White 0.060
0.691
Other
0.062
0.027
a. Verify that this is a legitimate probability model.
b. Let A be the event that a randomly chosen person is Hispanic, and let B be the
event that the person chosen is white.
a. Find P(A)
b. Find P(B)
c. Find P(A and B). Are these events mutually exclusive?
d. Suppose C is the event that a randomly chosen person is Asian.
i. Find P(C)
ii. Find P(A) + P(C)
iii. Find P(A and C). Are these events mutually exclusive?