Question

A pair of dice is rolled, and the numbers showing are observed. Find the probability of getting a sum of 9 or higher.

Answer 1

To find the probability of getting a sum of 9 or higher when rolling a pair of dice, we need to determine the number of favorable outcomes (when the sum of the two dice is 9 or higher) and the total number of possible outcomes.

There are 6 possible outcomes for each die, ranging from 1 to 6. Since we have two dice, the total number of possible outcomes is 6 * 6 = 36.

Now, let's determine the number of favorable outcomes, which is when the sum of the two dice is 9 or higher. We can list the combinations that satisfy this condition: (3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6).

Therefore, the number of favorable outcomes is 10.

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

Probability = Number of favorable outcomes / Total number of possible outcomes
= 10 / 36
= 5 / 18

Hence, the probability of getting a sum of 9 or higher when rolling a pair of dice is 5/18 or approximately 0.2778.

Answer 2

To find the probability of getting a sum of 9 or higher when rolling a pair of dice, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.

Step-by-step explanation:

To find the probability of getting a sum of 9 or higher when rolling a pair of dice, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.

There are a total of 36 possible outcomes when rolling two dice (6 possible outcomes for the first die and 6 possible outcomes for the second die). To get a sum of 9 or higher, we need either a sum of 9, 10, 11, or 12. The only way to get a sum of 9 is to roll a 3 on the first die and a 6 on the second die. The ways to get sums of 10, 11, and 12 are: 4+6, 5+5, 5+6, 6+4, 6+5, and 6+6.

So, there are a total of 7 favorable outcomes. The probability of getting a sum of 9 or higher is therefore 7/36, which is approximately 0.194 or 19.4%.