Table of Contents
- 1 How do you find the probability that A and B occur?
- 2 How do you find the probability that at least one event occurs?
- 3 Is it possible for a pair of random events to be both independent and mutually exclusive provide a clear justification for your answer?
- 4 How do you find the probability of at most one?
- 5 What is the probability of getting at least one six in a single throw of three unbiased dice?
- 6 How do you show two events are independent?
How do you find the probability that A and B occur?
Formula for the probability of A and B (independent events): p(A and B) = p(A) * p(B). If the probability of one event doesn’t affect the other, you have an independent event. All you do is multiply the probability of one by the probability of another.
How do you find the probability that at least one event occurs?
To calculate the probability of an event occurring at least once, it will be the complement of the event never occurring. This means that the probability of the event never occurring and the probability of the event occurring at least once will equal one, or a 100\% chance.
Is it possible for a pair of random events to be both independent and mutually exclusive provide a clear justification for your answer?
No, mutually exclusive events (with non-zero probability) are always dependent. The definition of independence for events A and B is that P(A and B) = P(A)P(B).
How do you do exactly one probability?
The probability that exactly one of the events A and B occur is P(A and not B) + P(not A and B). The events A and B are independent, so P(A and not B) = P(A)P(not B) = p(1 − q) = p − pq.
How do you calculate exactly one event occurring?
P(exactly one of them occurs) = P(A) + P(B)
How do you find the probability of at most one?
Hint. The easy way to do it: the probability that at most one event will occur is the same as the probability that not both will occur, that is, 1−P(A∩B) .
What is the probability of getting at least one six in a single throw of three unbiased dice?
Hence the probability of getting at least one six is 1 – 125216 = 91216. In a single throw of three dice, find the probability of getting the same number on all the three dice.
How do you show two events are independent?
Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true. You can use the equation to check if events are independent; multiply the probabilities of the two events together to see if they equal the probability of them both happening together.
Why can two events not be both independent and mutually exclusive?
If two events are mutually exclusive then they do not occur simultaneously, hence they are not independent. Thus, if event A and event B are mutually exclusive, they are actually inextricably DEPENDENT on each other because event A’s existence reduces Event B’s probability to zero and vice-versa.