170 students were asked whether they had read the ‘Bible’ (B), ‘The Lord of the Rings’ (L) or ‘War and Peace’ (W). 20 said they had read all three; 70 had read two but not all three; 35 had read none; 30 had read B and L but not W; 15 had read B and W not L; 60 had read W; 85 had read B. What is your probability that a randomly chosen student from his group has read The Lord of the Rings?
Answers
The probability that a chosen student has read Lord of the Rings = 10/17
Step-by-step explanation:
Let the sets are
B : Students who have read Bible
L : Students who have read Lord of the Rings
W : Students who have read War and Peace
Total students
n(S) = 170
According to the question
n(B ∩ L ∩ W) = 20
n(B ∩ L) + n(L ∩ W) + n(W ∩ B) - 3n(B ∩ L ∩ W) = 70
or, n(B ∩ L) + n(L ∩ W) + n(W ∩ B) = 70 + 3×20 = 130
35 students have read none of the books
∴ n(B ∪ L ∪ W) = n(S) - 35 = 170 - 35 = 135
n(B ∩ L) = 30
n(W ∩ B) = 15
∴ n(L ∩ W) = 70 - 30 - 15 = 25
n(W) = 60
n(B) = 85
We know that
n(B ∪ L ∪ W) = n(B) + n(L) + n(W) - n(B ∩ L) - n(L ∩ W) - n(W ∩ B) + n(B ∩ L ∩ W)
or, 135 = 85 + n(L) + 60 - 130 + 20
or, n(L) = 135 - 35 = 100
Students who have read Lord of the Rings = 100
Probability that a chosen student has read Lord of the Rings
= 100/170 = 10/17
Hope this answer is helpful.
Know More:
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