BTGModeratorVI wrote: ↑

Sat Jun 27, 2020 6:40 am

Vladimir plays a game in which he reveals cards one-at-a-time from the top of a shuffled standard deck of cards (consisting of 52 cards total: 13 in each of the four suits clubs, diamonds, hearts, and spades). If Vladimir reveals a heart, he wins. If he reveals a diamond, the game continues. If he reveals a club or a spade, he loses. What is the probability that Vladimir wins the game?

A. 1/4
B.13/51
C. 4/13
D. 1/3
E. 1/2

Answer: D
Source: Veritas Prep

One way to approach this question is to recognize that diamond cards have no effect on Vladimir winning or losing the game. When we get a diamond, we just move on to the next card.
So, if we remove all of the diamond cards from the deck, this will not alter the probability that Vladimir wins the game.
Once we remove all of the diamond cards from the deck, we have 39 cards remaining. 13 cards are hearts, 13 cards are clubs and 13 cards are spades.
At this point, the game will be won or lost on the FIRST DRAW.

So, P(Vladimir wins) = P(1st card is a heart) = 13/39 = 1/3

Answer: D

Cheers,
Brent

BTGModeratorVI wrote: ↑

Sat Jun 27, 2020 6:40 am

Vladimir plays a game in which he reveals cards one-at-a-time from the top of a shuffled standard deck of cards (consisting of 52 cards total: 13 in each of the four suits clubs, diamonds, hearts, and spades). If Vladimir reveals a heart, he wins. If he reveals a diamond, the game continues. If he reveals a club or a spade, he loses. What is the probability that Vladimir wins the game?

A. 1/4
B.13/51
C. 4/13
D. 1/3
E. 1/2

Answer: D

Solution:

We should observe that diamonds have no effect in this game; a diamond draw is simply followed by another draw. Therefore, the probability of winning is not affected if we remove all the diamond cards from the deck, leaving us with 39 cards (13 hearts and 26 clubs and spades). After removing the diamonds, Vladimir has 13/39 = 1/3 chance of drawing a heart and winning the game.

Answer: D