Podcast
Questions and Answers
Two events, C and D, are mutually exclusive. If P(C) = 0.3 and P(D) = 0.4, what is the probability of either C or D occurring?
Two events, C and D, are mutually exclusive. If P(C) = 0.3 and P(D) = 0.4, what is the probability of either C or D occurring?
- 0.7 (correct)
- 0.3
- 0.5
- 0.12
Events X and Y are not mutually exclusive. If P(X) = 0.6, P(Y) = 0.5, and P(X and Y) = 0.3, what is the probability of either X or Y occurring?
Events X and Y are not mutually exclusive. If P(X) = 0.6, P(Y) = 0.5, and P(X and Y) = 0.3, what is the probability of either X or Y occurring?
- 1.4
- 0.2
- 0.8 (correct)
- 0.3
A box contains both red and blue marbles. Event R is drawing a red marble, and event B is drawing a blue marble. Given that drawing a marble is either red or blue, what can be said about events R and B?
A box contains both red and blue marbles. Event R is drawing a red marble, and event B is drawing a blue marble. Given that drawing a marble is either red or blue, what can be said about events R and B?
- They both have the same probability.
- They are independent events.
- They are mutually exclusive. (correct)
- They are not mutually exclusive.
A student is enrolled in both a math class and a music class. What does it mean if selecting a student in the math class and selecting a student in the music class are not mutually exclusive events?
A student is enrolled in both a math class and a music class. What does it mean if selecting a student in the math class and selecting a student in the music class are not mutually exclusive events?
In a sample space S, events A and B are mutually exclusive. If $P(A) = 0.4$, what is the maximum possible value for $P(B)$?
In a sample space S, events A and B are mutually exclusive. If $P(A) = 0.4$, what is the maximum possible value for $P(B)$?
Events E and F are such that $P(E) = 0.5$, $P(F) = 0.3$, and $P(E \text{ or } F) = 0.8$. Are events E and F mutually exclusive, and why?
Events E and F are such that $P(E) = 0.5$, $P(F) = 0.3$, and $P(E \text{ or } F) = 0.8$. Are events E and F mutually exclusive, and why?
Consider two overlapping sets. Set A contains multiples of 3, and Set B contains multiples of 4. If a number is selected at random, what event would represent $P(A \text{ and } B)$?
Consider two overlapping sets. Set A contains multiples of 3, and Set B contains multiples of 4. If a number is selected at random, what event would represent $P(A \text{ and } B)$?
In a survey, 60% of people like coffee, 40% like tea, and 20% like both. What percentage of people like either coffee or tea?
In a survey, 60% of people like coffee, 40% like tea, and 20% like both. What percentage of people like either coffee or tea?
What distinguishes mutually exclusive events from events that are not mutually exclusive?
What distinguishes mutually exclusive events from events that are not mutually exclusive?
Given two events R and S, where $P(R) = 0.4$ and $P(S) = 0.6$. If it is known that $P(R \text{ or } S) = 0.7$, what is $P(R \text{ and } S)$?
Given two events R and S, where $P(R) = 0.4$ and $P(S) = 0.6$. If it is known that $P(R \text{ or } S) = 0.7$, what is $P(R \text{ and } S)$?
Flashcards
Mutually Exclusive Events
Mutually Exclusive Events
Events that cannot occur simultaneously. If one happens, the other cannot.
P(A or B) for Mutually Exclusive Events
P(A or B) for Mutually Exclusive Events
The probability of either event A or event B occurring is the sum of their individual probabilities.
Inclusive Events
Inclusive Events
Events where both can occur at the same time. The probability of A or B is the sum of their probabilities minus the probability of both occurring together.
P(A or B) for Inclusive Events
P(A or B) for Inclusive Events
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Study Notes
- Mutually exclusive events are events that cannot occur simultaneously.
- The probability of either mutually exclusive event A or B occurring is P(A or B) = P(A) + P(B)
- Events that can occur at the same time are inclusive events.
- The equation for calculating the probability of inclusive events is P(A or B) = P(A) + P(B) - P(A and B).
- Because counting the individual events will count the overlap twice, the overlap probability is subtracted to accurately reflect the probability.
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Description
Learn about mutually exclusive events, which cannot occur simultaneously, and inclusive events, which can. Explore probability calculations for both, including the formulas P(A or B) = P(A) + P(B) for mutually exclusive events and P(A or B) = P(A) + P(B) - P(A and B) for inclusive events.
