From the given Venn diagram the probability of getting P(A∩B∩C) is 1/25.
From the given Venn diagram we need to find P(A∩B∩C).
What is the use of the Venn diagram?
A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items.
Here, there are three circles that 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
So, 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
Now, n(A ∩ B ∩ C) = 2
∴ P(A ∩ B ∩ C) = 2/50 = 1/25
Therefore, from the given Venn diagram the probability of getting P(A∩B∩C) is 1/25.
To learn more about the Venn diagrams visit:
https://brainly.com/question/1605100.
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