P(A)=.37, P(B)=.19, P(A and B)=.13. What is the probability that A doesn't occur or B does?
To find the probability that either event A doesn't occur or event B occurs, we can use the formula:
P(A' or B) = P(A') + P(B) - P(A' and B)
First, let's find the probability of event A not occurring, denoted as A':
P(A') = 1 - P(A)
= 1 - 0.37
= 0.63
Next, we can substitute the given values into the formula to find the probability of either event A not occurring or event B occurring:
P(A' or B) = P(A') + P(B) - P(A' and B)
= 0.63 + 0.19 - P(A' and B)
To find the probability of A' and B occurring, denoted as A' and B, we can use the formula:
P(A' and B) = P(B) - P(A and B)
Substituting the given values:
P(A' and B) = 0.19 - 0.13
= 0.06
Now we can substitute this value back into the previous equation:
P(A' or B) = 0.63 + 0.19 - P(A' and B)
= 0.63 + 0.19 - 0.06
= 0.76
Therefore, the probability that either event A doesn't occur or event B occurs is 0.76, or 76%.