Question

Events A and B are independent. The probability that events A and B both occur is 0.6. What is the probability of event A?

Answer 1

Step-by-step explanation:

The events A and B are independent. The probability that event A occurs is 0.6, and the probability that at least one of the events A or B occurs is 0.94.

Answer 2

Answer:

The probability of event A is 0.4.

Step-by-step explanation:

If events A and B are independent, then the probability of both events A and B occurring is given by the product of their individual probabilities:

P(A and B) = P(A) * P(B)

We know that P(A and B) = 0.6, so we can write:

0.6 = P(A) * P(B)

Since we don't have information about P(B), we can't determine P(A) directly from this equation. However, we do know that the probability of A occurring, given that B has occurred, is simply P(A), since the events are independent. This is sometimes called the conditional probability of A given B and is denoted P(A|B). Using this notation, we can write:

P(A and B) = P(A|B) * P(B)

Since events A and B are independent, P(A|B) = P(A), so we have:

0.6 = P(A) * P(B)

We still don't know the value of P(B), but we can use the fact that the sum of the probabilities of all possible outcomes is 1 to find it:

P(A) + P(not A) = 1

Since events A and not A (the complement of A) are mutually exclusive and exhaustive, we have:

P(not A) = 1 - P(A)

Substituting this into the previous equation, we get:

0.6 = P(A) * P(B) = P(A) * (1 - P(A))

Solving for P(A), we have:

P(A)^2 - P(A) * 0.6 = 0

P(A) * (P(A) - 0.6) = 0

The solutions to this equation are P(A) = 0 and P(A) = 0.6. However, since we know that P(A and B) = 0.6, we must have P(A) < 0.6. Therefore, the only possible solution is:

P(A) = 0.4

So the probability of event A is 0.4.

To know more about independent event: https://brainly.in/question/17384050

To know more about conditional probability: https://brainly.com/question/27684587

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