If P(A)=0.5, P(B)=0.6 and P(A and B)=0.15, find the following probabilities:/
a) P(A or B)=
b) P(not A)=
c) P(not B)=
d) P(A and (not B))=
e) P(not (A and B))=
e) P(not (A and B)) = (1-.5)(1-.6) = ?
Use the same principles from here and your later post.
To find the probabilities, we can use the basic rules of probability. Here's how you can find the values for each of the provided probabilities:
a) P(A or B):
To find the probability of either event A or event B occurring, you can use the formula: P(A or B) = P(A) + P(B) - P(A and B).
In this case, P(A) = 0.5, P(B) = 0.6, and P(A and B) = 0.15.
So, substituting the values into the formula, we get:
P(A or B) = 0.5 + 0.6 - 0.15 = 0.95.
b) P(not A):
To find the probability of event A not occurring (complement of A), you can use the formula: P(not A) = 1 - P(A).
In this case, P(A) = 0.5.
So, substituting the value into the formula, we get:
P(not A) = 1 - 0.5 = 0.5.
c) P(not B):
To find the probability of event B not occurring (complement of B), you can use the formula: P(not B) = 1 - P(B).
In this case, P(B) = 0.6.
So, substituting the value into the formula, we get:
P(not B) = 1 - 0.6 = 0.4.
d) P(A and (not B)):
To find the probability of event A occurring and event B not occurring, you can use the formula: P(A and (not B)) = P(A) - P(A and B).
In this case, P(A) = 0.5 and P(A and B) = 0.15.
So, substituting the values into the formula, we get:
P(A and (not B)) = 0.5 - 0.15 = 0.35.
e) P(not (A and B)):
To find the probability of both event A and event B not occurring, you can use the formula: P(not (A and B)) = 1 - P(A and B).
In this case, P(A and B) = 0.15.
So, substituting the value into the formula, we get:
P(not (A and B)) = 1 - 0.15 = 0.85.
Therefore, the probabilities are:
a) P(A or B) = 0.95
b) P(not A) = 0.5
c) P(not B) = 0.4
d) P(A and (not B)) = 0.35
e) P(not (A and B)) = 0.85