How Can Ivan Achieve a Total Score of 5 with Three Dice?

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SUMMARY

To achieve a total score of 5 with three dice, the possible combinations are (1, 1, 3), (1, 2, 2), (2, 1, 2), (3, 1, 1), and permutations thereof. The total number of outcomes when rolling three dice is 216, leading to a probability of obtaining a total score of 5 calculated as 6 favorable outcomes divided by 216 total outcomes, resulting in a probability of 1/36. The discussion emphasizes the importance of systematically listing combinations to solve probability problems effectively.

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  • Understanding of basic probability concepts
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  • Knowledge of how to calculate outcomes for multiple dice
  • Ability to construct and interpret probability tables
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  • Learn how to calculate probabilities for multiple dice rolls
  • Study combinatorial mathematics for listing outcomes
  • Explore the concept of permutations and combinations in probability
  • Practice with examples of probability problems involving three or more dice
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Ivan throws three fair dice.

(i) List all the possible scores on the three dice which give a total score of 5, and hence show that
the probability of Ivan obtaining a total score of 5 is 1/36


MY PROBLEM HERE IS THAT I CANNOT LIST THE PROBABILITY OF POSSIBLE SCORE FOR THREE DICE, IN FACT FOR THE TWO DICE I KNOW THAT I HAVE TO CONTRUCT A TABLE BUT FOR THE 3 DICE I AM STUCK




HELPPPP THANKS IN ADVANCE
 
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Start by making a table with three columns

Die 1 Die 2 Die 3

then fill in the rows with all the ways to have the sides occur so that the sum is 5. You'll also need to calculate the total number of outcomes (number of ways three dice can come up: the number for 2 dice is 36 - you need the corresponding number for three dice)
 

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