Question

let a and b be two events. suppose the probability that neither a or b occurs is 2/3. what is the probability that one or both occur?

Answer 1

The probability that one or both occur (A and B occur, A occur B don't, or A don't occur B occur) is 1/3.

Probability

If there are two events, there is some probabilities:

• P(AB) : A occurs, B occurs (both occur)
• P(A) : A occurs, B don't occur (one occurs)
• P(B) : A don't occur, B occurs (one occurs)
• P(0) : A don't occur, B don't occur (neither A nor B occurs)

Probability of all probabilities (the sum of 4 probabilities) is 1.

From that 4 probability, we can convert it into mathematical form:

P(AB) + P(A) + P(B) + P(0) = 1

We know that neither A nor B occurs or P(0) is 2/3.

And probability that one or both occur means:

• P(AB) : A occurs, B occurs (both occur)
• P(A) : A occurs, B don't occur (one occurs)
• P(B) : A don't occur, B occurs (one occurs)

P(AB) + P(A) + P(B) + P(0) = 1

P(AB) + P(A) + P(B) + 2/3 = 1

P(AB) + P(A) + P(B)          = 1 - 2/3

P(AB) + P(A) + P(B)          = 1/3

Learn more about probability here: https://brainly.com/question/11234923

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