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)

Mithra asked you what P is. You didn't respond.

http://www.jiskha.com/display.cgi?id=1311880585

im not sure what P is....

P is probability: P(A|B) reads probability of event A given event B.

yes that's what it means, but im stuck on this problem....

To determine the values n(A), n(B), P(A), P(B), P(A|B), and P(B|A) using the given Venn diagram, you need to understand some basic concepts.

1. n(A) represents the number of items in set A. In this case, the number of items in set A is 50, as indicated by the number in the A part of the Venn diagram.

2. n(B) represents the number of items in set B. In this case, the number of items in set B is 110, as indicated by the number in the B part of the Venn diagram.

3. P(A) represents the probability of an event belonging to set A. To calculate this, you need to know the total number of items in the sample space. From the Venn diagram, we can see that the total number of items in both sets A and B is 140 (50 in A + 40 in the intersecting part + 50 in B). So, the probability of an event belonging to set A is P(A) = n(A) / Total = 50 / 140 = 0.357.

4. P(B) represents the probability of an event belonging to set B. Similarly, the probability of an event belonging to set B can be calculated using the total number of items in the sample space. P(B) = n(B) / Total = 110 / 140 = 0.786.

5. P(A|B) represents the conditional probability of an event belonging to set A given that it already belongs to set B. To calculate this, we need to divide the number of items in the intersection of A and B by the number of items in set B. From the Venn diagram, we can see that the number of items in the intersection of A and B is 40. So, P(A|B) = n(A āˆ© B) / n(B) = 40 / 110 = 0.364.

6. P(B|A) represents the conditional probability of an event belonging to set B given that it already belongs to set A. To calculate this, we need to divide the number of items in the intersection of A and B by the number of items in set A. From the Venn diagram, we can see that the number of items in the intersection of A and B is 40. So, P(B|A) = n(A āˆ© B) / n(A) = 40 / 50 = 0.8.

So, the values are:
n(A) = 50
n(B) = 110
P(A) = 0.357
P(B) = 0.786
P(A|B) = 0.364
P(B|A) = 0.8