Suppose A and B are events with P (A)=0.25, P(A or B)=0.5, and P (A and B )=0.07. Find each of the following.
a. P(B)=0.07/0.25=.28
b. P (not B)=
Please help me I need the steps to solve the question
P(A or B) = P(A) + P(B) - P(A and B)
plug in your values, you are given 3 of the 4
To find P(B), we can use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
Given that P(A or B) = 0.5, P(A) = 0.25, and P(A and B) = 0.07, we can substitute these values into the formula:
0.5 = 0.25 + P(B) - 0.07
Next, we can isolate P(B):
0.5 - 0.25 + 0.07 = P(B)
0.32 = P(B)
Therefore, P(B) = 0.32.
To find P(not B), we can use the complement rule which states that P(not B) = 1 - P(B).
Substituting the value of P(B) we just found, we get:
P(not B) = 1 - 0.32
P(not B) = 0.68
Therefore, P(not B) is equal to 0.68.
In summary:
a. P(B) = 0.32
b. P(not B) = 0.68