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Together with the 48 cases you counted we would have 48+60=108 ways to get the sum of 10 or less, so the probability is 1-108/216=1/2.īunuel I know this can be a lengthy,but can you show how the different combinations of 9 is equal to 25 I am getting 28Īlso the different combinations of 10 I am getting 36 well as it should be 27 Outcomes where Joe scores more than 10 = 216 - 48 = 168 , 18), or more then the average, is the same as to get the sum less than average (10, 9, 8. Mary scored 10 so the probability to get the sum more then 10 (11, 12, 13. The sum of 18 - 1 (notice equals to the combinations of the sum of 3). The sum of 17 - 3 (notice equals to the combinations of the sum of 4) The sum of 16 - 6 (notice equals to the combinations of the sum of 5) The sum of 15 - 10 (notice equals to the combinations of the sum of 6) The sum of 14 - 15 (notice equals to the combinations of the sum of 7) The sum of 13 - 21 (notice equals to the combinations of the sum of 8) The sum of 12 - 25 (notice equals to the combinations of the sum of 9) The sum of 11 - 27 (notice equals to the combinations of the sum of 10) Since we know that the probability of getting more than 10 (11, 12. How can we solve it using the same expected value approach? What if the question is to find out the probability of the sum to be greater than 12? Thus the probability of getting the sum from 3 to 10 = the probability of getting the sum from 11 to 18 = 1/2. The probability of getting the sum of 10 = the probability of getting the sum of 11

The probability of getting the sum of 5 = the probability of getting the sum of 16 The probability of getting the sum of 4 = the probability of getting the sum of 17 The probability of getting the sum of 3 (min possible sum) = the probability of getting the sum of 18 (max possible sum) That's because the probability distribution is symmetrical for this case: If Mary scores 10 in her attempt what is the probability that Joe will outscore Mary in his?Įxpected value of one die is 1/6*(1+2+3+4+5+6)=3.5.Įxpected value of three dice is 3*3.5=10.5. The score is the sum of points on all three dice. Mary and Joe are to throw three dice each.