Question

A sample space S is given as S = {1, 2, 3, 4, 5,6, 7}
Following events are described for this sample space.
Event X = {1,2,3}
Y = {3,4,5}
Z = {5,6}
Events X , Y and Z are exhaustive events.

• A. True
• B. False

Answer 1

The correct option is B False

Exhaustive, the word in itself is self-explanatory. Isn’t it? It should “exhaust” the sample space.
Do events X, Y and Z do it? Let’s check.
X = {1,2,3}
Y = {3,4,5}
Z= {5,6}
When we take their union it comes out to be {1,2,3} U {3,4,5} U {5,6} = {1,2,3,4,5,6}

Oops!! 7 is missing which is there in the sample space. If 7 was there, it would have been exhaustive. But it’s missing sadly. They are not exhaustive.