Cards are selected one at a time without replacement from a well-shuffled deck of 52 cards until an ace is drawn. Let X denote the random variable that gives the number of cards drawn. What values may X assume?
A) X may assume the values in the set S = {1, 2, ...,52}
B) X may assume the values in the set S = {1, 2, ...,47}
C) X may assume the values in the set S = {1, 2, ...,48}
D) X may assume the values in the set S = {1, 2, ...,49}

Question

Cards are selected one at a time without replacement from a well-shuffled deck of 52 cards until an ace is drawn. Let X denote the random variable that gives the number of cards drawn. What values may X assume? ​
A) X may assume the values in the set S = {1, 2, ...,52}
B) X may assume the values in the set S = {1, 2, ...,47}
C) X may assume the values in the set S = {1, 2, ...,48}
D) X may assume the values in the set S = {1, 2, ...,49}

Quizplus · Accepted Answer

Since there are four aces in a standard deck of 52 cards, the first ace can appear on the first card drawn or the 48th card drawn (if it hasn't appeared in the first 47 cards drawn). Therefore, X can take on values in the set S = {1, 2, ..., 49} and the best choice is D).

Cards Are Selected One at a Time Without Replacement from a Well-Shuffled