Event-Based Questions and Letter Probability
Let's solve the event-based questions from the image provided.
A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet. So we have tiles labeled A, B, C, D, E, F, G.
Event X: The letter selected is found in the word 'BAG'.
The outcomes for Event X are: B, A, G.
Event Y: The letter selected comes after 'C'.
The outcomes for Event Y are: D, E, F, G.
Now let's answer the parts of the question:
(a) Event "X or Y": This is the union of events X and Y, meaning the letter is in 'BAG' or comes after 'C'.
The outcomes are: A, B, G (from Event X) and D, E, F, G (from Event Y). Combined without duplicates, we get:
A, B, D, E, F, G
(b) Event "X and Y": This is the intersection of events X and Y, meaning the letter is both in 'BAG' and comes after 'C'.
The outcome is: G (since G is the only letter in both sets).
(c) The complement of the event X: This is the set of outcomes that are not in Event X.
Since Event X has A, B, and G, the complement of Event X is the set of letters not in 'BAG' but within the first seven letters of the alphabet.
The outcomes are: C, D, E, F.
