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If you roll two fair six-sided dice, what is the probability that the sum is 5 or lower?

If you roll two fair six-sided dice, what is the probability that the sum is 55 or lower?

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Full solution

Q. If you roll two fair six-sided dice, what is the probability that the sum is 55 or lower?
  1. Count Dice Outcomes: Count all possible outcomes for rolling two dice. Each die has 66 faces, so there are 6×6=366 \times 6 = 36 possible outcomes.
  2. Identify Sum 55 or Less: Identify the outcomes where the sum is 55 or less. These are (1,1)(1,1), (1,2)(1,2), (1,3)(1,3), (1,4)(1,4), (2,1)(2,1), (2,2)(2,2), (2,3)(2,3), (3,1)(3,1), (3,2)(3,2), and (4,1)(4,1).
  3. Count Favorable Outcomes: Count the number of favorable outcomes. There are 1010 outcomes where the sum is 55 or less.
  4. Calculate Probability: Calculate the probability. Probability = Number of favorable outcomes / Total number of outcomes = 1036\frac{10}{36}.
  5. Simplify Fraction: Simplify the fraction. 1036\frac{10}{36} can be simplified to 518.\frac{5}{18}.

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