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
Given:
Total students= 170
Students reading all three= 20
Students reading only two but not three = 70
Students reading none= 35
Students reading only B+L = 30
Students reading only B+W = 15
Students reading W= 60
Students reading B= 85
To find:
The probability that a randomly chosen student from his group has read The Lord of the Rings
Solution:
Students reading at least one book= 170-35 = 135
Students reading only L+W= 70- (20+30+15) = 5
Students reading only W= 60-(20+15+5)= 20
Students reading only B= 85-(30+20+15) = 20
So, students reading only L= 135-(20+20+5+20+15+30) = 25
So, students reading L= 25+5+20+30 = 80
The probability that a randomly chosen student from his group has read The Lord of the Rings= Number of students reading L/Total students= 80/170 =8/17
The probability that a randomly chosen student from his group has read The Lord of the Rings is 8/17.
