Consider the Venn diagram below. The numbers in the regions of the circle indicate the number of items that belong to that region.

(2 intersecting circles A & B, where A part is 50, B part is 110, and the intersecting part is 40)

Determine:

n(A)
n(B)
P(A)
P(B)
P(A|B)
P(B|A)

How in the world do i input this in my calculator?? I have no idea how to do this...

To find the answers to these questions, you can use the following formulas and steps:

n(A): To determine n(A), you need to find the sum of the numbers in the region that belongs to set A. In this case, n(A) = 50.

n(B): Similarly, to find n(B), you sum up the numbers in the region belonging to set B. Here, n(B) = 110.

P(A): To calculate the probability of event A, you divide the number of elements in set A (n(A)) by the total number of elements, which is the sum of n(A), n(B), and the intersecting part, which is 40 in this case. So, P(A) = n(A)/(n(A) + n(B) + intersecting part) = 50 / (50 + 110 + 40) = 50 / 200 = 0.25.

P(B): Similarly, you calculate the probability of event B by dividing the number of elements in set B (n(B)) by the total number of elements. So, P(B) = n(B) / (n(A) + n(B) + intersecting part) = 110 / (50 + 110 + 40) = 110 / 200 = 0.55.

P(A|B): To calculate the probability of A given B (P(A|B)), you divide the number of elements in both A and B by the number of elements in B. In this case, P(A|B) = intersecting part / n(B) = 40 / 110 = 0.36.

P(B|A): Lastly, you calculate the probability of B given A (P(B|A)) by dividing the number of elements in both A and B by the number of elements in A. So, P(B|A) = intersecting part / n(A) = 40 / 50 = 0.8.

To input these calculations into your calculator, you can follow the steps above and use the appropriate buttons on your calculator to perform the necessary calculations.