G When a pair of dice is rolled there are 36 different possible outcomes: 1-1, 1-2, ... 6-6. If a pair ofdice is rolled 3 times, what is the probability of getting a sum of 4 every time

The probability of getting a sum of 4 every time is 1/12

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Total number of outcomes possible when a pair of dice is rolled = 36

2. If a pair of dice is rolled 3 times, what is the probability of getting a sum of 4 every time.

Let's build the number of times for each outcome, this way:

Value of X  Number of outcomes

2                      1 (1,1)

3                      2 (1,2), (2,1)

4                      3 (1,3), (2,2), (3,1)

5                      4 (1,4), (2,3), (3,2), (4,1)

6                      5 (1,5), (2,4), (3,3), (4,2), (5,1)

7                      6 (1,6), (2,4), (3,4), (4,3), (5,2), (6,1)

8                      5 (2,6), (3,5), (4,4), (5,3), (6,2)

9                      4 (3,6), (4,5), (5,4), (6,3)

10                     3 (4,6), (5,5), (4,6)

11                      2 (5,6), (6,5)

12                     1 (6,6)

Let's recall the formula of probability:

Probability = Number of favorable outcomes/Total number of possible outcomes

Replacing with the information we know:

Probability =3/36 = 1/12

The probability of getting a sum of 4 every time is 1/12

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