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

1/12 is the probability of getting sum of 4 everytime

Step-by-step explanation:

The Probability of getting the sum of 4 when a dice is rolled is 1/12. In a sample space of 36, only 3 occurrence lead to sum of 4 (1,3) (2,2) and (3,1).

For each time the dice is rolled, the Probability of sum 4 is 1/12.