The numbers in the Venn diagram below represent the number of elements in each a

Question

The numbers in the Venn diagram below represent the number of elements in each area. Example: The number of elements in A and B and C is 1. a) How many elements are in the set A? _____ b) How many elements are in B or C? _____ c) How many elements are in A but not C? _____ d) How many elements are in A or B or C? _____ e) How many elements are in neither A nor B nor C? f) How many elements are in U? _____ If P(A) = .7, P(B) = .45 and P(A and B) = .2, a. P(A or B) = _____ b. P(not A) = _____ c. P(not B) = _____ d. PA and not B) = _____ e. P(A and B)' = P(not(A and B)) = _____ If A and B are two mutually exclusive events with P(A) = .25 and P(B) = .65, a) P(A and B) = _____ b) P(A or B) = _____ c) P(not A) = _____ d) P(not B) = _____ e) P(not (A or B)) = _____ f) P(A and not B) = _____

Explanation / Answer

Question 3:

a) From the given venn diagram we can easily count the number of elements in each set. Number of elements in set A are: 2 + 2 + 1 + 4 = 9

b) Number of elements in B or C are: 3 +4 +1 + 5 + 2 +7 = 22

c) Number of elements in A but not in C = 2 + 4 = 6

d) Number of elements in A or B or C means that we have to count all the elements in the whole diagram except the 6 elements which are outside the 3 circles. Therefore answer would be: 2 + 2 + 1 + 4 + 3 + 5 + 7 = 24

e) Number of elements in neither A nor B nor C are 6 that are outside the 3 circles.

f) Number of elements in U are the sum of all the elements = 2 + 2 + 1 + 4 + 3 + 5 + 7 +6 = 30

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.