Answer:
A) The sample space(S) = {hc, mc, lc, ht, mt, lt}
B) Outcome in A1 ={c, t}
C) Outcomes in A2 = {hc, mc, lc}
D) Outcomes in A3 = {hc, ht, lc, lt}
Ei) No, A1, A2 and A3 are not mutually exclusive.
Eii) Yes, A1, A2 and A3 are collectively exhaustive
Explanation:
A) First of all, from the question, there will be 6 elements in the sample space. These are;
- 3{high(h), medium (m), low(l)} which correspond to mouse click(c)
- 3{high(h), medium(m), low(l)} which corresponds to tweet (t).
Thus, we can say that the sample space(S) = {hc, mc, lc, ht, mt, lt}
B) For A1 to correspond to medium speed connection, it means it must have 2 outcomes which are; mouse click (c) and tweet (t)
Thus, A1 ={c, t}
C) For A2 to be the event mouse click (c), it will have 3 outcomes namely;
High click, medium click and low click.
So A2 = {hc, mc, lc}
D) For A3 to be the event "high speed connection or low speed connection, we will have 4 outcomes which are 2 each of high and low speed connection. These are ;
So A3 = {hc, ht, lc, lt}
E) i) For A1, A2 and A3 to be mutually exclusive, it will result in an empty set. This can be expressed as;
A1 ∩ A2 ∩ A3 = Φ
Now, looking at the results for A1, A2 and A3 above, we can see that no single item appears in the 3 of them at the same time.
Thus, A1 ∩ A2 ∩ A3 = Φ
E) ii) For A1, A2 and A3 to be collectively exhaustive, the result of A1 U A2 ∪ A3 has to contain every possible member in the sample space (S).
Thus, we can write it as A1 U A2 ∪ A3 = S
Now, A1 U A2 ∪ A3 = {hc, ht, mc, mt, lc, lt}
Since A1 U A2 ∪ A3 results in a set that contains all the members of the sample space, A1, A2 and A3 are collectively exhaustive
