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18 Nov 2018, 23:22
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
28% (02:27) correct
72%
(02:12)
wrong
based on 230
sessions
History
Date
Time
Result
Not Attempted Yet
Patty and Selma play a gambling game in which Patty rolls a single fair six-sided die, numbered 1 through 6, and Selma rolls a single fair ten-sided die, numbered 1 through 10. If they tie, they reroll. Otherwise, the player with the higher number wins the loser’s bet. If Patty bets $5, how much should Selma bet to make the bet fair (so that each player will, on average, win the same amount of money)?
A. $8.33
B. $12
C. $13
D. $15
E. $18
A. $8.33
B. $12
C. $13
D. $15
E. $18
20 Nov 2018, 00:12
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Bunuel
Total cases = 6 * 10 = 60
Cases in which Patty wins = 1 + 2 + 3 + 4 + 5 = 15
Patty 2, Selma 1
Patty 3, Selma 1/2
...
Patty 6, Selma 1/2/3/4/5
Case in which no one wins = 6 (Both throw the same number 1/2/3/4/5/6)
Cases in which Selma wins = 60 - 15 - 6 = 39
Since Patty wins in 15 cases and Selma wins in 39, they should bet money in the same ratio so that they win an equal amount on average.
If Patty bets $5, Selma should bet $13.
Answer (C)
Bunuel
Chance of Patty's winning:
Suppose Selma rolls 1, then patty can win in5 different ways:by rolling one of 2,3,4,5, or 6
If Selma rolls 2, then patty can win in 4 different ways: by rolling one of 3,4,5, or 6
So we can conclude Patty can win in 5 + 4 + 3 + 2 + 1 = 15 different ways.
So probability of Patty's winning = \(\frac{15}{(6 * 10)}\) = \(\frac{15}{60}\)
[Here \(6 * 10 = 60\) is the number of total events that can occur by rolling a 6 sided dice and a 10 sided dice]
Chance of Selma's winning:
Suppose Patty rolls 1, then Selma can win in 9 different ways:by rolling one of 2,3,4,5,6,7,8,9,10
If Selma rolls 2, then Selma can win in 8 different ways:by rolling one of 3,4,5,6,7,8,9,10
Similarly we can conclude Selma can win in 9 + 8 + 7 + 6 + 5 + 4 = 39 different ways.
So probability of Selma's winning = \(\frac{39}{(6 * 10)}\) = \(\frac{39}{60}\).
As Patty bets $5 when Selma wins, Selma gets that $5. Let's assume Selma bets x amount of dollars. According to the question each player must win same amount in average. So we can say that,
\(x * \frac{15}{60} = 5 * \frac{39}{60}\)
\(x = 5 * \frac{39}{15} = 13\)
So C is the answer
General Discussion
19 Nov 2018, 03:16
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Bunuel
Good question took me over 2 mins to solve i hope that answer is correct...
P of Patty winning is 1/6 a
P of Selma winning is 1/6 *4/10 ; 4/60 : as she has 10 sided die so (7,8,9,10) are all her winning no.
Avg of winning of both : 4/60+1/6= 14/60= 7/30
and avg of loosing the game of both =23/30
so the amount which needs to be added so as to have a fair bet = (23/30)*5= 3.33 additional amount
so total amount which Selma would have to add is 5+3.33 $= 8.33 $ option A IMO...
GMATinsight : sir please check if the working & answer is okay or any other alternate solution is available for this question...
