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# Mary and Joe are to throw three dice each. The score is the

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Mary and Joe are to throw three dice each. The score is the [#permalink]

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23 Mar 2008, 12:23
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Mary and Joe are to throw three dice each. The score is the sum of points on all three dice. If Mary scores 10 in her attempt what is the probability that Joe will outscore Mary in his?

A. 24/64
B. 32/64
C. 36/64
D. 40/64
E. 42/64

OPEN DISCUSSION OF THIS QUESTION IS HERE: mary-and-joe-are-to-throw-three-dice-each-the-score-is-the-126407.html
[Reveal] Spoiler: OA

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Re: PS - Three dice... [#permalink]

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23 Mar 2008, 13:11
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B

fast 30-sec approach:

1. the average score for three dices is: 3.5*3=10.5
2. one half of Joe possible scores will be less than 10 or equal, other half of Joe possible scores will be greater than 11 or equal.
3. B
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Re: PS - Three dice... [#permalink]

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23 Mar 2008, 18:47
walker wrote:
B

fast 30-sec approach:

1. the average score for three dices is: 3.5*3=10.5
2. one half of Joe possible scores will be less than 10 or equal, other half of Joe possible scores will be greater than 11 or equal.
3. B

My god, math killer Walker! 30-sec approach

from where does 3.5 derive?
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Re: PS - Three dice... [#permalink]

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23 Mar 2008, 20:23
sondenso wrote:
from where does 3.5 derive?

1,2,3,4,5,6 ---> average=(1+2+3+4+5+6)/6=3.5
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Re: Mary and Joe are to throw three dice each. The score is the [#permalink]

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12 Oct 2013, 23:36
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Re: Mary and Joe are to throw three dice each. The score is the [#permalink]

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13 Oct 2013, 01:54
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Mary and Joe are to throw three dice each. The score is the sum of points on all three dice. If Mary scores 10 in her attempt what is the probability that Joe will outscore Mary in his?

A. 24/64
B. 32/64
C. 36/64
D. 40/64
E. 42/64

Expected value of one die is 1/6*(1+2+3+4+5+6)=3.5.
Expected value of three dice is 3*3.5=10.5.

Mary scored 10 so the probability to get the sum more then 10 (11, 12, 13, ..., 18), or more then the average, is the same as to get the sum less than average (10, 9, 8, ..., 3) = 1/2 = 32/64.

That's because the probability distribution is symmetrical for this case:
The probability of getting the sum of 3 (min possible sum) = the probability of getting the sum of 18 (max possible sum);
The probability of getting the sum of 4 = the probability of getting the sum of 17;
The probability of getting the sum of 5 = the probability of getting the sum of 16;
...
The probability of getting the sum of 10 = the probability of getting the sum of 11;

Thus the probability of getting the sum from 3 to 10 = the probability of getting the sum from 11 to 18 = 1/2.

Also discussed here: mother-mary-comes-to-me-86407.html

OPEN DISCUSSION OF THIS QUESTION IS HERE: mary-and-joe-are-to-throw-three-dice-each-the-score-is-the-126407.html\
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Re: Mary and Joe are to throw three dice each. The score is the   [#permalink] 13 Oct 2013, 01:54
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