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%.