According to the venn diagram below, what is (image below)

a. 3/25
b. 4/25
c. 2/25
d. 1/25

P(A ∩ B ∩ C) is 1/25 ⇒ answer D

Step-by-step 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