If Enid and Topanga each roll a single ten-sided die (which has sides

Question

If Enid and Topanga each roll a single ten-sided die (which has sides numbered 1 through 10), what is the probability that Enid will roll a larger number than Topanga does?

A. 2/5
B. 9/20
C. 49/100
D. 99/200
E. 1/2

Shubhranil88 · Accepted Answer

The number of ways Enid and Topanga can roll a dice is 10C1 x 10C1 = 100.
The number of ways both get the same number = 10
Total number of ways in which they get different numbers= 100-10= 90
In these 90 outcomes half will have Enid with a greater number and half will have Topanga with a greater number.
Hence the number of favourable outcomes where Enid will have a larger number = 90 /2 = 45
Hence Probability = 45/100 = 9/20

0akshay0 · Answer

possible outcomes for each roll a single ten-sided die for Enid and Topanga are as follows Enid 1 2 3 4 5 6 7 8 9 10 Topanga 1 2 3 4 5 6 7 8 9 10 If Topanga gets a 1 there are 9 possible outcomes where Enid will roll a larger number than Topanga If Topanga gets a 2 there are 8 possible outcomes where Enid will roll a larger number than Topanga . . . If Topanga gets a 9 there is 1 possible outcome where Enid will roll a larger number than Topanga so total possibilities where Enid will roll a larger number than Topanga = 1+2+3+4+5+6+7+8+9 = 45 Total possibilities = 100 probability that Enid will roll a larger number than Topanga does = 45/100 = 9/20 Hence Option B is Correct Hit Kudos if you liked it 8-)

BillyZ · Answer

Official solution from Veritas Prep.

This problem combines two different ideas central to higher-level probability questions: pairs probability, and bad outcome counting.

We begin by noting that there are really three types of outcomes here: Enid rolls a larger number, Topanga rolls a larger number, or the two of them tie.

To calculate the probability of a tie, we use pairs probability; take the die rolls one at a time and ask, at each step, “am I still happy?” Since we’re going for a pair, any first roll will make us happy – every number is the first half of some possible pair. When the time comes for the second roll, on the other hand, we only have a  \frac{1}{10}  chance of being happy – we have to match whatever number was rolled before. So overall there is a  1∗\frac{1}{10}=\frac{1}{10}  chance of a tie, and a  1-\frac{1}{10}=\frac{9}{10}  chance that one die roll will be larger than the other.

To calculate the probability that Enid rolls a larger number, observe that it is equally as likely that Enid will win as it is that Topanga will win; there’s perfect symmetry between the two possibilities. So the probability that Enid will roll a larger number is simply half of the probability that someone will roll a higher number. That is,

P(Enid)=\frac{1}{2}∗\frac{9}{10}=\frac{9}{20} . This is  B .

onamarif · Answer

There are three possibilities Enid=Topanga Enid>Topanga EnidTopanga Enid

iliavko · Answer

this is a clear 700!

laxpro2001 · Answer

Not the hardest but here is one of those high level problems where you can bank some time for later ones by truly understanding the concept.

First I calculated the number of potential outcomes which is 10 * 10 = 100;

Next, figure out how many different ways in which a tie can occur which is just the number of possibilities where Enid's number equals Topanga which would be the total number of distinct outcomes (1, 2, 3, ... 10) which is 10;

Finally, its important to understand that without any special rules, outside of ties, the remaining possibilities are either wins or losses for Enid. Since they have equal probability of rolling each number, they are just as likely to win as they are to lose, one-half of the remaining outcomes represents the probability of a loss (as well as a win) for each of them:

100 - 10 = 90 possible non-tie outcomes;

90 / 2 = 45 possible outcomes where Enid wins;

45/100 --> reduce by 5 and you end up with 9/20, answer choice B;

GyMrAT · Answer

Total # of outcomes when 2, 10 sided dice are rolled = 10 * 10 = 100

Favorable Condition, Enid rolls a larger # than Topanga.
Hence we have, below possibilities,
Enid = 10 Topanga = 9, 8, 7,....1 = 9 possibilities
Enid = 9 Topanga = 8,7,6,......1 = 8 possibilities

.
.
.
Enid = 2 Topanga = 1 = 1 possibility

Total # of possibilities = 9+8+7+...+1 = 45

Required Probability = 45/100 = 9/20

Answer B.

Thanks,
GyM

EgmatQuantExpert · Answer

Solution

Given  
 • Enid and Topanga each roll a single ten-sided dice.

To find  
 • The probability that Enid will roll a larger number than Topanga.

Approach and Working out  
 • Total possibility = 10 * 10 = 100
• Number of cases when Enid will roll a larger number than Topanga.

o Enid get 10, Topanga can get 9 numbers (1, 2, 3, 4, 5, 6, 7, 8, 9) on his dice.
o Enid get 9, Topanga can get 8 numbers (1, 2, 3, 4, 5, 6, 7, 8) on his dice.
o Enid - 8, Topanga - 7 
o Enid - 7, Topanga - 6 
o Enid - 6, Topanga - 5 
o Enid - 5, Topanga - 4 
o Enid - 4, Topanga - 3 
o Enid - 3, Topanga - 2 
o Enid - 2, Topanga - 1 
o Enid - 1, Topanga - 0

So, total 1+2+3+4+5+6+7+8+9 = 45 cases.

• Hence, probability = 45/100 = 9/20

Hence, option C is the correct answer.

Correct Answer: Option C

BrushMyQuant · Answer

If Enid and Topanga each roll a single ten-sided die (which has sides numbered 1 through 10)

As we are rolling two dice => Number of cases =  10^2  = 100

What is the probability that Enid will roll a larger number than Topanga does?

Out of these 100 cases following can be the outcome:

Both rolls are equal, number of cases = 10  
 
 Remaining cases = 100 - 10 = 90  
 
 First roll > Second Roll = 90/2 = 45 cases 
 Second Roll > First Roll = 90/2 = 45 cases

=>  Probability that Enid will roll a larger number than Topanga  = 45/100 = 9/20

So,  Answer will be B 
Hope it helps!

Watch the following video to learn How to Solve Dice Rolling Probability Problems

https://www.youtube.com/watch?v=5PVZYQXet18

bumpbot · Answer

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If Enid and Topanga each roll a single ten-sided die (which has sides

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