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Why is the probability of intersection of two events subtracted in the sum of the events?
Wiki User
∙ 10y ago
The short answer is that if you don't do so, the intersection is double counted. The longer answer follows:
Suppose you have two events A and B which overlap. Then,
Event A = (only A happens) and (both A and B happen).
These two are mutually exclusive so that P(A) = P(A only) + P(both).
Similarly, P(B) = P(B only) + P(both).
Now, the event that A or B happen is the event that only A happens or only B happens or both happen.
That is, P(A or B) = P(A only) + P(both) + P(B only)
Adding and subtracting P(both) gives
P(A or B) = P(A only) + P(both) + P(B only) + P(both) - P(both)
Now, the first two are P(A) and the next two are P(B)
So P(A or B) = P(A) + P(B) - P(both).
Wiki User
∙ 10y ago
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How can you find the probability of two mutually exclusive events?
The calculation is equal to the sum of their probabilities less the probability of both events occuring. If two events are mutually exclusive then the combined probability that one or the other will occur is simply the sum of their respective probabilities, because the chance of both occurring is by definition zero.
What is the probability that the sum of the faces is 7?
The probability that the sum of two dice is 7 is 6 in 36, or 1 in 6.Of all the combinations, this is the one with the highest probability.
What is addition and multiplication theorems on probability with examples?
When considering the probability of two different events or outcomes, it is essential to clarify whether they are mutually exclusive or independent. If the events are mutually exclusive, then the probability that either one or the other will occur equals the sum of their individual probabilities. This is known as the law of addition. If, however, two or more events or outcomes are independent, then the probability that both the first and the second will occur equals the product of their individual probabilities. This is known as the law of multiplication.
When two dice are rolled what is the probability of getting a sum of 9?
P(9) ≈ 11.11%When two dice are rolled there are 36 equiprobable events.The number of events that produce a sum of 9 are 4: (6,3), (5,4), (4,5) and (3,6).So the probability of getting a sum of 9 is, P(9) = 4/36 = 1/9 = 0.1111.... ≈ 0.1111≈ 11.11%
When rolling two dice what is the probability the sum is greater than 1?
The probability is 1.
Why is the probability of the intersection of two events subtracted in the sum of the probability of two events?
rghrugfy
How can you find the probability of two mutually exclusive events?
The calculation is equal to the sum of their probabilities less the probability of both events occuring. If two events are mutually exclusive then the combined probability that one or the other will occur is simply the sum of their respective probabilities, because the chance of both occurring is by definition zero.
Is it true that the probability of the union of two events id the sum of the probabilities of those events?
yes P(AUB)=P(A)+P(B) but only for mutualy exclusive events
What is the sum of probability that something will happen and the probability that something will NOT happen?
The sum is 1
What is a sum in probability?
The sum of the probability of success and the probability of failure had better equal 1.00 (100%) or an error has been committed.
How do you do probability of independent events?
The answer depends on what you mean by "do". Does it mean calculate individually, calculate the probability of either one or the other (or both), calculate the probability of both, calculate some function of both (for example the sum of two dice being rolled)?
What is the conditional expectation function?
It is the integral (or sum) of the joint probability distribution function of the two events, integrated over the domain in which the condition is met.
What is the probability that the sum is a prime number?
The answer depends on the sum of WHAT!
What is the probability that the sum of the faces is 7?
The probability that the sum of two dice is 7 is 6 in 36, or 1 in 6.Of all the combinations, this is the one with the highest probability.
When two dice are rolled find the probability of getting a 6 or 7?
Probability that the sum is 6 = 5/36 Probability that the sum is 7 = 6/36
What is addition and multiplication theorems on probability with examples?
When considering the probability of two different events or outcomes, it is essential to clarify whether they are mutually exclusive or independent. If the events are mutually exclusive, then the probability that either one or the other will occur equals the sum of their individual probabilities. This is known as the law of addition. If, however, two or more events or outcomes are independent, then the probability that both the first and the second will occur equals the product of their individual probabilities. This is known as the law of multiplication.
What is the probability of not rolling sum of 6 with two fair dice?
The probability of not rolling a sum of six with two fair dice is 1 minus the probability of rolling a sum of six. There are 36 permutations of rolling two dice. Of these, five sum to six, 1+5, 2+4, 3+3, 4+2, and 5+1. The probability, then of rolling a sum of six is 5 in 36. The probability, then of not rolling a sum of six is 31 in 36, or about 0.8611.
