Suppose A and B are events with P(A)=1/6, P(B)=5/6 and P(A and B)=1/12. Find each of the following
a. P(AorB)=
Formula: P(A)+P(B)-P(A&B)
1/6+5/6-1/12=11/12
b. P(not A)
1-1/6=5/6
c.P(not B)=
1-1/12=11/12
I am lost here can please correct any mistakes I did with my calculation and please show me the steps.Thank You.
Your calculations are correct! Here are the steps for each question:
a. To find P(A ∪ B) (probability of A or B), you can use the formula:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Given:
P(A) = 1/6
P(B) = 5/6
P(A ∩ B) = 1/12
Substitute these values into the formula:
P(A ∪ B) = (1/6) + (5/6) - (1/12)
To simplify this, you'll need a common denominator:
P(A ∪ B) = (2/12) + (10/12) - (1/12)
Now add the numerators and keep the denominator the same:
P(A ∪ B) = 11/12
Therefore, P(A ∪ B) = 11/12.
b. To find P(not A), you can use the complement rule:
P(not A) = 1 - P(A)
Given:
P(A) = 1/6
Substitute this value into the formula:
P(not A) = 1 - (1/6)
Simplify the right side of the equation:
P(not A) = (6/6) - (1/6)
Now subtract the numerators and keep the denominator the same:
P(not A) = 5/6
Therefore, P(not A) = 5/6.
c. To find P(not B), you can also use the complement rule:
P(not B) = 1 - P(B)
Given:
P(B) = 5/6
Substitute this value into the formula:
P(not B) = 1 - (5/6)
Simplify the right side of the equation:
P(not B) = (6/6) - (5/6)
Now subtract the numerators and keep the denominator the same:
P(not B) = 1/6
Therefore, P(not B) = 1/6.
So, your calculations are correct! P(A ∪ B) = 11/12, P(not A) = 5/6, and P(not B) = 1/6.