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 is found in the word \bag\. event y: the letter selected comes after \c\. 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 \x and y\: (b) event \x or y\: (c) the complement of the event x:

Explanation:

Step1: Determine the elements of each event

• The first seven letters of the alphabet are \(A, B, C, D, E, F, G\).
• Event \(X\): Letters in "BAG" are \(A, B, G\).
• Event \(Y\): Letters after "C" are \(D, E, F, G\).

Step2: Find \(X\) and \(Y\)

• \(X\cap Y\) (Event "X and Y"): Common elements of \(X\) and \(Y\).
• \(X\cap Y=\{G\}\)

Step3: Find \(X\) or \(Y\)

• \(X\cup Y\) (Event "X or Y"): All elements in \(X\) or \(Y\) or both.
• \(X\cup Y = \{A, B, D, E, F, G\}\)

Step4: Find the complement of \(X\)

• \(\overline{X}\) (Complement of \(X\)): Elements not in \(X\).
• \(\overline{X}=\{C, D, E, F\}\)

Answer:

(a) \(G\)
(b) \(A,B,D,E,F,G\)
(c) \(C,D,E,F\)