Two six sided dice numbered 1-6 on each thrown simultaneously, what is the orobabolity that the sum of the two sides are greater than nine?
out of the 36 possible outcomes, the number of cases greater than 9 are:
4-6, 6-4, 5-5 , 6-5, 5-6, 6-6
prob(your event) = 6/36 = 1/6
To calculate the probability that the sum of two six-sided dice is greater than nine, we need to determine how many possible outcomes satisfy this condition and divide it by the total number of possible outcomes.
Step 1: Determine the favorable outcomes
The possible outcomes that satisfy the condition "the sum of the two sides is greater than nine" are as follows:
- Rolling a 4 on the first die and a 6 on the second die: (4, 6)
- Rolling a 5 on the first die and any number greater than or equal to 5 on the second die: (5, 5), (5, 6)
- Rolling a 6 on the first die and any number greater than or equal to 4 on the second die: (6, 4), (6, 5), (6, 6)
Step 2: Count the total number of outcomes
The total number of outcomes when two six-sided dice are thrown is given by the product of the number of outcomes on each die, which is 6 * 6 = 36.
Step 3: Calculate the probability
To find the probability, we divide the number of favorable outcomes (6) by the total number of outcomes (36):
Probability = Favorable outcomes / Total outcomes = 6 / 36 = 1 / 6
Therefore, the probability that the sum of the two sides is greater than nine is 1/6.
To find the probability that the sum of the two dice is greater than nine, we need to determine the number of favorable outcomes and the total number of possible outcomes.
To get started, let's identify the favorable outcomes. In this case, the only possible sums that are greater than nine are 10, 11, and 12.
Next, let's determine the total number of possible outcomes. Since each die has six sides, there are 6 possible outcomes for one die and 6 possible outcomes for the other die. Therefore, the total number of possible outcomes is 6 x 6 = 36.
Now, we need to count the number of favorable outcomes.
For a sum of 10:
- Possible outcomes: (4, 6), (5, 5), (6, 4) (3 outcomes)
For a sum of 11:
- Possible outcomes: (5, 6), (6, 5) (2 outcomes)
For a sum of 12:
- Possible outcome: (6, 6) (1 outcome)
So, there are a total of 3 + 2 + 1 = 6 favorable outcomes.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
= 6 / 36
= 1 / 6
≈ 0.1667 or 16.67%
Therefore, the probability that the sum of the two sides of the dice is greater than nine is approximately 1/6 or 16.67%.