Instructor Katherine Cliff
Which of the following statements is false?
A. Two disjoint events cannot occur at the same time.
B. Two independent events cannot occur at the same time.
C. Two complementary events cannot occur at the same time.
Identify whether the events are disjoint, independent, or neither. Be prepared to explain your choices.
A. You and a randomly selected student from your class both earn A’s in this course.
B. You and your class partner both earn A’s in this course.
If two events can occur at the same time, they must be independent. True or False?
When tackling a probability problem, ask yourself…
For an “AND” situation…
If so,
If not,
For an “OR” situation…
Are the events disjoint?
If so,
If not,
Example 1
Suppose that in a random sample of 210 college students, a survey finds that 125 like bacon, 135 like chocolate, 130 like coffee, 90 like bacon and chocolate, 85 like coffee and chocolate, 65 like bacon and coffee, and 50 like all three. If a member of this senior class is selected at random, find the probability that the student: a) Likes bacon but not chocolate, b) Doesn’t like bacon or coffee
Jailee is going to graduate from a biomedical engineering department by the end of the semester. After being interviewed at two companies he likes, he guesses that his probability of getting an offer from company A is 0.75 and his probability of getting an offer from company B is 0.60. If he further believes that the probability that he will get offers from both companies is 0.5, what is the probability that he will get an offer from neither of these two companies?
Given that \(P(A)=0.6\), \(P(B) = 0.3\), and \(P(A\cup B)=0.85)\), find the following:
\[P(A \cap B) = \]
Given that \(P(A)=0.6\), \(P(B) = 0.3\), and \(P(A\cup B)=0.85)\), find the following:
\[P((A \cap B)^C) = \]
Given that \(P(A)=0.6\), \(P(B) = 0.3\), and \(P(A\cup B)=0.85)\), find the following:
\[P(A^C \cap B) = \]
A discrete probability distribution is…
| A | B | C | D | E | |
|---|---|---|---|---|---|
| Probability | 0.3 | 0.5 | 0.5 | 0.2 | 0.1 |
| A | B | C | D | E | |
|---|---|---|---|---|---|
| Probability | 0.3 | 0.5 | 0.2 | 0.1 | -0.1 |
| A | B | C | D | E | |
|---|---|---|---|---|---|
| Probability | 0.2 | 0.6 | 0 | 0.1 | 0.1 |
Example 3
If we roll a pair of dice three times in a row, what is the probability that we’ll get at least one set of doubles?
That’s numbers 5 through 8 in the notes packet.