SOLUTION: I need help if someone can help me with just these three problems and please explain them to me step by step because i am having difficulty with them....I would greatly appreciated

Question 86682: I need help if someone can help me with just these three problems and please explain them to me step by step because i am having difficulty with them....I would greatly appreciated it...
Problem #1
Draw a vendiagram and use the given information to fill in the number of elements for each region.
n (A ' ) = 28 , n(B) = 25, n (A' U B ' ) = 45, n(A (upside down U ) B )=12
Problem #2
Let A and B independent events with P (A) = (1)/(4) and P(B) = (1)/(5).
Find P(A (Upside down U) B) and P(A U B)
Problem #3
In the previous section, we described an experiment in which the numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacement. Find each probability
The probability that the first number is 3, given the following.
a. The sum is 7.
b. The sum is 8.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Draw a vendiagram and use the given information to fill in the number of elements for each region.
n (A ' ) = 28 , n(B) = 25, n (A' U B ' ) = 45, n(A (upside down U ) B )=12
-----
Draw two intersecting circles inside a rectangle.
Label them A and B.
Put a 12 in the intersection of A and B.
Since B has 25 put 25-12 = 13 in the remaining section of B.
Since A' is 28 put a 28-13 = 15 in the rectangle but in neither circle.
Since (A' OR B') = (A and B)' put 45-(13+15)=17 in the unnumbered region
of A.
---------------
Problem #2
Let A and B independent events with P (A) = (1)/(4) and P(B) = (1)/(5).
Find P(A (Upside down U) B)
since A and B are independent the answer is (1/4)(1/5) = 1/20
-----------------
P(A U B) = P(A)+P(B)-P(A intersect B) = 1/4 + 1/5 - 1/20 = 8/20 = 2/5
-------------------
Problem #3
In the previous section, we described an experiment in which the numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacement. Find each probability
The probability that the first number is 3, given the following.
a. The sum is 7.
b. The sum is 8.
-------
Answered Previously.
=====================
Cheers,
Stan H.

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