Answer:
(a) 5/7 chance
(b) 2/7 chance
(c) 5/7 chance
Step-by-step explanation:
Event X: There are 3 letters that come before "D". A, B, and C. There is a 3 out of 7 chance of picking one of those letters. (3/7)
Event Y: There are 4 letters in "C A G E". Those 4 letters are in the 7 first letters of the alphabet meaning that they are in our pile of tiles. There is a 4 out of 7 chance of picking one of those letters. (4/7)
(a) Since there is a 3/7 chance of Event X happening and a 4/7 chance of Event Y happening, there is a 5/7 chance of either Event X or Event Y happening since tiles "A" and "C" are included in both events.
(b) Since there is a 3/7 chance of Event X happening and a 4/7 chance of Event Y happening, there is a 2/7 chance of both X and Y happening since there are only 2 tiles that are the same in both events, "A" and "C". (We are only allowed to pick one tile)
(c) The complement of Event Y is 1-4/7=5/7 chance.
