Question

A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet.

The letter selected will be recorded as the outcome.

Consider the following events.

Event

X

: The letter selected comes before "

D

".
Event

Y

: The letter selected is found in the word "

CAGE

".

Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.

(a) Event"XorY": (b) Event"XandY": (c) The complement of the event X :

Answer 1

Given that a tile is selected from seven tiles, each labelled with a different letter from the first seven letters of the alphabet. Thus, the event of seven tiles is known as the universal set. Let the set of first seven letters be denoted by "S". Thus, S = {A, B, C, D, E, F, G}

Now, Event X = The letter selected comes before D. Thus, X = {A, B, C}.

Event Y = The letter selected is found in the word "CAGE". Thus, Y = {A, C, E, G}.

a) Here, we have to find Event "X or Y". Thus, we have to find (X Y). Thus, (X Y) = {A, B, C, E, G}

Thus, Event "X or Y" = {A, B, C, E, G}.

b) Here, we have to find Event "X and Y". Thus, we have to find (X Y). Thus, (X Y) = {A, C}.

Thus, Event "X and Y" = {A, C}.

c) Here, we have to find the complement of the event X. Thus, we have to find . We know, consists of elements which are not present in X but present in S [As, we know, X+=S].

Thus, = S - X = {D, E, F, G}.

Thus, = {D, E, F, G}.

Thus, the complement of the event X = {D, E, F, G}.