Two dice are rolled. What is the probability that the two numbers add up to a prime number?


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Answer:

 

15
36
 

Step by Step Explanation:
  1. The two dice that are rolled can show any of these values.
    Dice 1: 1, 2, 3, 4, 5, 6.
    Dice 2: 1, 2, 3, 4, 5, 6.
    So, we can get a total of 36 combinations between them (6 × 6).
  2. If we take one value from the list of possible values from each Dice, we get numbers ranging from 2 (when both Dice show 1) to 12. (when both dice show 6)
    Let's enumerate the prime numbers between 2 and 12. They are 2, 3, 5, 7 and 11.
    We need to see in how many ways we can get each of these values.
    Let's put the value rolled by the dice as (x, y), where x is the value rolled by Dice 1, and y the value rolled by Dice 2.
    - 2: The only way to get this is when we roll (1, 1). 1 possibility.
    - 3: We can get this by (1, 2) or (2, 1). 2 possibilities.
    - 5: We can get this by (2, 3), (3, 2), (1, 4) or (4, 1). 4 possibilities.
    - 7: We can get this by (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1). 6 possibilities.
    - 11: We can get this by (5, 6), or (6, 5). 2 possibilities
    This gives us a total of 1 + 2 + 4 + 6 + 2 = 15 possible ways to get a prime number.
  3. So, the probability of getting the two numbers add up to a prime is  
    15
    36
     .

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