what is the probability of rolling a sum that exceeds 4 with two dice

Let's take a look at what we DON"T want

We do not want sums of 2, 3 and 4
sum of 2 -- 1 way
sum of 3 -- 2 ways
sum of 4 -- 3 ways , for a total of 6 we do not want
Since the two dice can fall in 36 ways,
30 of them would exceed a sum of 4

prob(your event) = 30/36 = 5/6

To find the probability of rolling a sum that exceeds 4 with two dice, we can calculate the number of favorable outcomes and divide it by the total number of possible outcomes.

Let's consider the possible outcomes of rolling two dice:

Dice 1: 1, 2, 3, 4, 5, 6
Dice 2: 1, 2, 3, 4, 5, 6

To exceed a sum of 4, we need the sum to be 5 or greater. We can list the possible outcomes that meet this condition:

Sum of 5: (1, 4), (2, 3), (3, 2), (4, 1)
Sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1)
Sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)
Sum of 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2)
Sum of 9: (3, 6), (4, 5), (5, 4), (6, 3)
Sum of 10: (4, 6), (5, 5), (6, 4)
Sum of 11: (5, 6), (6, 5)
Sum of 12: (6, 6)

Counting the favorable outcomes, we have a total of 30 outcomes.

Now let's determine the total number of possible outcomes. Since we have two dice, each with 6 possible outcomes, the total number of outcomes is 6 * 6 = 36.

To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:

Probability = Favorable outcomes / Total outcomes
Probability = 30 / 36
Probability β‰ˆ 0.8333

Therefore, the probability of rolling a sum that exceeds 4 with two dice is approximately 0.8333 or 83.33%.

To calculate the probability of rolling a sum that exceeds 4 with two dice, we need to first determine the total number of possible outcomes. Then, we will find the number of outcomes that satisfy the given condition, and finally, divide that by the total number of possible outcomes.

Step 1: Determine the total number of possible outcomes.
When rolling two dice, each die can take on 6 different values: 1, 2, 3, 4, 5, or 6. Since we have two dice, the total number of outcomes is obtained by multiplying the number of possible outcomes for each die together. Therefore, the total number of possible outcomes is 6 x 6 = 36.

Step 2: Find the number of outcomes that exceed 4.
To find the number of outcomes that exceed 4, we can list all the possible combinations of the dice rolls that satisfy the condition. These combinations are: (2, 3), (3, 2), (2, 4), (4, 2), (3, 3), (3, 4), (4, 3), (4, 4), (5, 2), (5, 3), (5, 4), (6, 2), (6, 3), (6, 4), (6, 5). Counting these combinations, we find that there are 15 outcomes that exceed 4.

Step 3: Calculate the probability.
To find the probability, we divide the number of outcomes that satisfy the condition (15) by the total number of possible outcomes (36):

Probability = Number of outcomes that exceed 4 / Total number of possible outcomes
= 15 / 36
= 5 / 12
β‰ˆ 0.4167

Therefore, the probability of rolling a sum that exceeds 4 with two dice is approximately 0.4167 or about 41.67%.