Section 1 - Mutually exclusive events. Flashcards
What are mutually exclusive events?
Events that cannot occur at the same time.
If event A occurs, what can be said about event B if A and B are mutually exclusive?
Event B cannot occur.
True or False: The events ‘rolling a 3’ and ‘rolling a 4’ on a fair six-sided die are mutually exclusive.
True.
Fill in the blank: The probability of mutually exclusive events A and B occurring is calculated as _____ the probability of A and the probability of B.
the sum of.
What is the formula for finding the probability of either event A or event B occurring if they are mutually exclusive?
P(A or B) = P(A) + P(B).
If P(A) = 0.5 and P(B) = 0.3, what is P(A or B) if A and B are mutually exclusive?
P(A or B) = 0.8.
True or False: Mutually exclusive events can have a joint probability greater than zero.
False.
What is an example of two mutually exclusive events?
Flipping a coin and getting heads or tails.
Is it possible for two events to be mutually exclusive and dependent at the same time?
No, mutually exclusive events are independent.
If two events are not mutually exclusive, what does that imply?
They can occur at the same time.
What does it mean if the probability of A and B is zero?
A and B are mutually exclusive.
Multiple Choice: Which of the following pairs of events are mutually exclusive? A) Rolling a 2 or rolling an even number B) Drawing a heart or drawing a spade.
B) Drawing a heart or drawing a spade.
Fill in the blank: The sum of the probabilities of all mutually exclusive outcomes in a sample space equals _____ .
1.
What is the complement of a mutually exclusive event?
An event that includes all outcomes not in the original event.
True or False: If two events are mutually exclusive, the occurrence of one event guarantees the non-occurrence of the other.
True.
If P(A) = 0.4 and P(B) = 0.5, can A and B be mutually exclusive?
No, because their probabilities sum to more than 1.
What happens to the probability of event A if event B occurs and they are mutually exclusive?
The probability of A remains unchanged.
Multiple Choice: Which scenario illustrates mutually exclusive events? A) Drawing a red card or a black card B) Rolling a 5 or rolling a number less than 5.
A) Drawing a red card or a black card.
What is the probability of getting a 1 or a 6 when rolling a fair six-sided die?
P(1 or 6) = P(1) + P(6) = 1/6 + 1/6 = 1/3.
True or False: The events ‘being born male’ and ‘being born female’ are mutually exclusive.
True.
What is the key characteristic of mutually exclusive events?
They cannot happen at the same time.
Fill in the blank: The probability of event A occurring is denoted as _____ .
P(A).
What is the combined probability of mutually exclusive events if one has a probability of 0.2 and the other has a probability of 0.5?
0.7.
Multiple Choice: Which of the following is NOT a mutually exclusive event? A) Winning the lottery or losing the lottery B) Choosing a red apple or a green apple.
B) Choosing a red apple or a green apple.
If two events are independent, can they be mutually exclusive?
No, independent events can occur together.
What is the probability of rolling a die and getting either a 2 or a 5?
1/3.
True or False: Mutually exclusive events can overlap.
False.
What does it mean if two events are exhaustive?
They cover all possible outcomes in the sample space.
Multiple Choice: If P(A) = 0.1 and P(B) = 0.2, what is P(A and B) if they are mutually exclusive? A) 0.3 B) 0 C) 1.
B) 0.
