If events E and F are disjoint mutually exclusive and the ev

If events E and F are disjoint (mutually exclusive) and the events F and G are disjoint, must the events E and G necessarily be disjoint? Give an example to illustrate your opinion. Choose the correct answer below.

A.Yes, events E and G must be disjoint. For example, E = {0,1,2}, F = {3,4,5}, and G= {6,7,8} show that E and F are disjoint events, F and G are disjoint events, and E and G are also disjoint events.

B.No, events E and G are not necessarily disjoint. For example, E = {0,1,2}, F = {3,4,5}, and G = {2,6,7} show that E and F are disjoint events, F and G are disjoint events, and E and G are events that are not disjoint.

C.Yes, events E and G must be disjoint. For example, E = {0,1,2}, F = {3,4,5}, and G = {2,6,7} show that E and F are disjoint events, F and G are disjoint events, and E and G are also disjoint events.

D.No, events E and G are not necessarily disjoint. For example, E = {0,1,2}, F = {3,4,5}, and G = {6,7,8} show that E and F are disjoint events, F and G are disjoint events, and E and G are events that are not disjoint.

Solution

we are given that

events E and F are disjoint (mutually exclusive)

the events F and G are disjoint

There can be some common element between E and G

so, No, events E and G are not necessarily disjoint

Because

if we have

E = {0,1,2}, F = {3,4,5}, and G = {2,6,7}

It means that E and F are disjoints and F and G are also disjoints

But E and G are not disjoint because they have common element 2

so, second option is right answer