In a game with one die, player X wins if the number of points on her

Question

In a game with one die, player X wins if the number of points on her throw is greater than,or equal to, the number of points on player Y’s throw. The probability of X winning is:

(A) 1/2
(B) 19/36
(C) 13/24
(D) 7/12
(E) 2/3

gmatcafe · Answer

There are 6*6=36 ways of choosing pairs of X and Y. Let's consider the number of ways in which Y may win. If Y=2, in order Y to win X must be 1. If Y=3, X must be be 1 or 2. If Y=4, X must be 1, 2 or 3 and so on:
Y:2 3 4 5 6
 1 2 3 4 5 
In 1+2+3+4+5=15 ways Y wins. In 36-15=21 ways X wins. 21/36=7/12 D)

BAA5 · Answer

Outcome of Y...................Probability of Y .............Probability of X

.......... 1 ................................1/6...........................6/6
.......... 2 ................................1/6 ..........................5/6 
.......... 3 ................................1/6 ...........................4/6
.......... 4 ...............................1/6........................... 3/6
.......... 5 ................................1/6............................2/6
.......... 6 ................................1/6 ...........................1/6

Probability of X winning is (1/6)(6/6 + 5/6 + 4/6 +3/6 + 2/6 +1/6) = 21/36 = 7/12

JerryAtDreamScore · Answer

Breaking Down the Info:

There are  6 * 6 = 36  outcomes in total.

The probability of X and Y tying, would be  \frac{6}{36} = \frac{1}{6} .

We can divide the rest of the probability space in half as the probability of X throwing higher than Y is the same as the probability of Y throwing higher than X.

Then the probability of X getting a higher throw is  \frac{5}{6}/2 = \frac{5}{12} . Finally add  \frac{1}{6}  back as a tie counts as X winning.

\frac{5}{12} + \frac{2}{12} = \frac{7}{12} .

Answer: D

AJSIPA · Answer

Total no. of pairs of (x,y)=6*6=36

x>=y

(1,1), (2,1), (3,1), (4,1), (5,1), (6,1)=6 ways
(2,2), (2,3), (2,4), (2,5), (2,6)=5 ways
.
.
((6,6)=1 way

Similarly, we add up 6+5+4+3+2+1=21

Probability of x wining is =21/36=7/12

In a game with one die, player X wins if the number of points on her

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In a game with one die, player X wins if the number of points on her

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