Vladimir plays a game in which he reveals cards one-at-a-time

BTGModeratorVI wrote: ↑

Fri Apr 10, 2020 8:10 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

Awesome question!

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