Question

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​

Answer 1

Given :  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

To find : probability that a randomly chosen student from his group has read The Lord of the Rings

Solution:

Total = 170

All 3  ( B ∩ L ∩ W)  = 20

70 had read two but not all three;

(B ∩ L ) + (L ∩ W) + (B ∩  W) -  3  ( B ∩ L ∩ W)  = 70

=> (B ∩ L ) + (L ∩ W) + (B ∩  W)  =  130

Read None  = 35

30 had read B and L but not W;   => (B ∩ L)  -   ( B ∩ L ∩ W)  = 30

=> B ∩ L = 50

15 had read B and W not L => (B ∩  W)   -   ( B ∩ L ∩ W)  = 15

=> (B ∩  W) = 35

(B ∩ L ) + (L ∩ W) + (B ∩  W)  =  130

=> 50 + (L ∩ W) + 35  =  130

=> (L ∩ W)  = 45

60 had read W  => W = 60

85 had read B. => B = 85

Total = L + B + W  - ( (B ∩ L ) + (L ∩ W) + (B ∩  W) ) +  ( B ∩ L ∩ W)   + none

=> 170 = L + 85 + 60  - 130 + 20  + 35

=> L = 100

probability that a randomly chosen student from his group has read The Lord of the Rings​  = 100/170

= 10/17

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