Answer:
P(A ∩ B ∩ C) is 1/25 ⇒ answer D
Explanation:
* Lets talk about the Venn diagram
- There are three circles intersect each other
- The number of elements ∈ (A ∩ B) and ∉ C = 5
∴ n(A ∩ B) and ∉ C = 5
- The number of elements ∈ (A ∩ C) and ∉ B = 6
∴ n(A ∩ C) and ∉ B = 6
- The number of elements ∈ (C ∩ B) and ∉ A = 4
∴ n(C ∩ B) and ∉ A = 4
- The number of elements ∈ (A ∩ B ∩ C) = 2
∴ n(A ∩ B ∩ C) = 2
- The number of elements ∈ A and ∉ B , C = 9
- The number of elements ∈ B and ∉ A , C = 8
- The number of elements ∈ C and ∉ A , B = 7
- The number of elements ∉ A , B , C = 9 ⇒ outside the circles
- The total elements in the Venn diagram is the sum of all
previous numbers
∴ The total number in the Venn diagram = 5 + 6 + 4 + 2 + 9 + 8 + 7 + 9 =
50
* To find the probability of (A ∩ B ∩ C), find the total number in
the Venn diagram and the number of elements in the intersection
part of the three circles
∵ The total elements in the Venn diagram = 50 elements
∵ n(A ∩ B ∩ C) = 2
∴ P(A ∩ B ∩ C) = 2/50 = 1/25
* P(A ∩ B ∩ C) is 1/25