Two six-sided dice are rolled at the same time and the numbers showing are observed. Find the following.
a. P(sum=8)
(5,2) (2,5)
2/36
Please help me with the steps
Possible ways to get a sum of 8:
2,6 ; 6,2 ; 5,3 ; 3 5, 4,4
there are 5 of these
so P(sum = 8) = 5/36
I don't understand what your (5,2) and (2,5) are supposed to represent.
To find the probability of getting a sum of 8 when rolling two six-sided dice, you need to determine the number of favorable outcomes (where the sum is 8) and the total number of possible outcomes.
Step 1: Determine the favorable outcomes.
To obtain a sum of 8, you can have the following combinations:
- A roll of 2 on the first die and 6 on the second
- A roll of 3 on the first die and 5 on the second
- A roll of 4 on the first die and 4 on the second
- A roll of 5 on the first die and 3 on the second
- A roll of 6 on the first die and 2 on the second
Step 2: Calculate the number of favorable outcomes.
Since each die has six sides, there are 6 possible outcomes for each die. Thus, the total number of favorable outcomes is 5 (as calculated in Step 1).
Step 3: Determine the total number of possible outcomes.
When rolling two dice, there are 36 possible outcomes. This is because there are 6 possible outcomes for the first die and 6 possible outcomes for the second die, resulting in a total of 6 x 6 = 36 possible outcomes.
Step 4: Calculate the probability.
To find the probability, divide the number of favorable outcomes by the total number of possible outcomes:
Probability = favorable outcomes / total outcomes
Probability = 5 / 36
Therefore, the probability of obtaining a sum of 8 when rolling two six-sided dice is 5/36.