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....

I believe the answer to be P(A/B)

You just need to draw the diagram.

yes but i cannot draw how the diagram looks, so i typed how it looks....see above in parenthesis :)

To determine n(A) and n(B), you need to add up the values in their respective regions. From the Venn diagram you provided, n(A) is 50 and n(B) is 110.

To calculate the probabilities P(A) and P(B), you need to divide the number of items in each set by the total number of items in the entire sample space. In this case, the sample space is the combination of both sets A and B.

The total number of items in the sample space can be found by adding the individual values in all the regions of the Venn diagram. In this case, it is n(A) + n(B) + intersecting part = 50 + 110 + 40 = 200.

So, P(A) = n(A) / total number of items = 50 / 200 = 0.25 or 25%
And, P(B) = n(B) / total number of items = 110 / 200 = 0.55 or 55%

To calculate the conditional probabilities P(A|B) and P(B|A), you need to use the formula:

P(X|Y) = P(X ∩ Y) / P(Y)

Where X and Y represent events or sets.

From the Venn diagram, you can see that the intersecting part (X ∩ Y) has a value of 40.

To calculate P(A|B):
P(A|B) = P(A ∩ B) / P(B)
P(A ∩ B) is the value in the intersecting part, which is 40.
P(B) is the probability of B, which we calculated earlier as 0.55.

So, P(A|B) = 40 / 110 = 0.3636 or approximately 36.36%

Similarly, to calculate P(B|A):
P(B|A) = P(B ∩ A) / P(A)
Here, P(B ∩ A) is the value in the intersecting part, which is 40.
P(A) is the probability of A, which we calculated earlier as 0.25.

So, P(B|A) = 40 / 50 = 0.8 or 80%

As for inputting this into your calculator, you may want to use parentheses to ensure the order of operations is correct. For example, to calculate P(A|B), you would input 40 ÷ 110 into your calculator and then divide the result by 0.55.