The probability that an event A occurs is P(A) = 0.3 . The event B is independent of A and P(B) = 0.4 .

a) Calculate P(A or B or both occur) .

Thanks in advance for the help!

Thanks for the reply! I get that the "a)" might have made it seem like a multiple choice question, but it's not, you gotta calculate the answer using the info given above. According to the answers, it's supposed to be 0.58, but what I need to know is how to get there.

I've always thought that "or" means you add the probabilities up. So that would mean 0.4 + 0.3 + 0.4 x 0.3 = 0.82 but that obviously isn't the answer. Could someone explain how to get 0.58?

Thanks in advance

To calculate the probability that event A or B or both occur, we can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

Since events A and B are independent, the probability of both occurring (P(A and B)) is simply the product of their individual probabilities:

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

Let's substitute the given values into the formula:

P(A or B) = P(A) + P(B) - P(A) * P(B)

P(A or B) = 0.3 + 0.4 - (0.3 * 0.4)

P(A or B) = 0.3 + 0.4 - 0.12

P(A or B) = 0.7 - 0.12

P(A or B) = 0.58

Therefore, the probability that event A or B or both occur is 0.58.

To calculate the probability that either event A or B or both occur, you need to use the concept of "probability of union".

The probability of the union of two events A and B is given by the formula:

P(A or B) = P(A) + P(B) - P(A and B)

Since event A and B are independent, the probability of the intersection (A and B) is simply the product of their individual probabilities:

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

Given that P(A) = 0.3 and P(B) = 0.4, you can substitute these values into the formula to find the probability of the union of A and B:

P(A or B) = P(A) + P(B) - P(A and B)
= 0.3 + 0.4 - (0.3 * 0.4)
= 0.3 + 0.4 - 0.12
= 0.58

Therefore, the probability that event A or B or both occur is 0.58, or 58%.

P(A) or (B) or (both) = P(A) + P(B) - [P(A) * P(B)]