A, b and c are three students who attend the same tutorial classes. if the probability that on a particular day exactly one out of a and b attends the class is 7/10; exactly one out of b and c attends is 4/10; exactly one out of c and a attends is 7/10. i
Answers
Given : A, b and c are three students who attend the same tutorial classes. the probability that on a particular day exactly one out of a and b attends the class is 7/10; exactly one out of b and c attends is 4/10; exactly one out of c and a attends is 7/10
To Find : All of three attends
Solution:
exactly one out of a and b attends the class
a - a∩b + b - a∩b
= a + b - 2a∩b = 7/10
exactly one out of b and c attends the class
= b + c - 2b∩c = 4/10
exactly one out of c and a attends the class
= a + c - 2a∩c = 7/10
=> 2 (a + b + c - a∩b - b∩c - a∩c ) = 7/10 + 4/10 + 7/10
=> a + b + c - a∩b - b∩c - a∩c = 0.9
1 = a + b + c - a∩b - b∩c - a∩c + a∩b∩c
=> 1 = 0.9 + a∩b∩c
=> a∩b∩c = 0.1
All of three attends probability = 1/10
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