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 solve this problem using your calculator, you first need to understand some basic probability concepts.
n(A) represents the number of items in set A.
n(B) represents the number of items in set B.
P(A) represents the probability of an event A occurring.
P(B) represents the probability of an event B occurring.
P(A|B) represents the probability of event A occurring given that event B has occurred.
P(B|A) represents the probability of event B occurring given that event A has occurred.
To find n(A) and n(B), you will use the numbers given in the Venn diagram. In this case, n(A) = 50 and n(B) = 110, as indicated in the diagram.
To find P(A) and P(B), you need to divide the number of items in each set by the total number of items. The total number of items can be found by adding the number of items in set A (50) and set B (110), and then subtracting the number in the intersection (40).
So, the total number of items = n(A) + n(B) - intersection = 50 + 110 - 40 = 120.
Therefore, P(A) = n(A) / total number = 50 / 120 ≈ 0.4167.
And P(B) = n(B) / total number = 110 / 120 ≈ 0.9167.
To find P(A|B) and P(B|A), you will use the probabilities of the individual events and the number in the intersection. Since P(A|B) represents the probability of A occurring given that B has occurred, you will divide the number in the intersection by the total number in B.
P(A|B) = intersection / n(B) = 40 / 110 ≈ 0.3636.
Since P(B|A) represents the probability of B occurring given that A has occurred, you will divide the number in the intersection by the total number in A.
P(B|A) = intersection / n(A) = 40 / 50 = 0.8.
To input these calculations in your calculator, you can use the following steps:
- Divide the number in set A by the total number to get P(A).
- Divide the number in set B by the total number to get P(B).
- Divide the number in the intersection by the number in set B to get P(A|B).
- Divide the number in the intersection by the number in set A to get P(B|A).
Make sure to use parentheses or brackets when entering calculations to ensure the correct order of operations.