Two six-sided dice are rolled at the same time and the numbers showing are observed. Find the following.
a. (P=sum of 8)
2 dice: (3,5) (5,3), (2,6), (6,2)
c. P(sum is an odd number)
2 dice (1,5) (3,3) (5,1)
I am lost here please help me with the further steps this is not in my textbook and my notes are confusing me.
There are 36 total possible combinations.
a. 2 dice: (3,5), (5,3), (2,6), (6,2),(4,4) = 5/36
c. None of them sum to an odd number. To sum to an odd number, each dice must have one odd number and one even number e.g., (1,2), (1,4)...(3,2) etc.....
To find the probabilities, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.
a. Probability of getting a sum of 8:
There are 4 favorable outcomes: (3,5), (5,3), (2,6), (6,2)
There are 36 possible outcomes since each die has 6 possible outcomes.
So, the probability is 4/36 or 1/9.
c. Probability of getting a sum that is an odd number:
There are 3 favorable outcomes: (1,5), (3,3), (5,1)
There are 36 possible outcomes.
So, the probability is 3/36 or 1/12.
Therefore,
a. P(sum of 8) = 1/9.
c. P(sum is an odd number) = 1/12.
To calculate the probability of rolling a specific sum with two six-sided dice, you need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
a. P(sum of 8)
The favorable outcomes for a sum of 8 are:
- (3,5)
- (5,3)
- (2,6)
- (6,2)
These represent the different combinations of rolling the dice and getting numbers that add up to 8. There are a total of 4 favorable outcomes.
The total number of possible outcomes when rolling two six-sided dice is calculated by considering that each die has 6 possible outcomes. So, there are 6 options for the first die and 6 options for the second die, resulting in a total of 6 * 6 = 36 possible outcomes.
Therefore, to find the probability of rolling a sum of 8, divide the number of favorable outcomes (4) by the total number of possible outcomes (36):
P(sum of 8) = 4/36 = 1/9
This can be simplified to approximately 0.1111 or 11.11% chance of rolling a sum of 8.
c. P(sum is an odd number)
The favorable outcomes for a sum of an odd number are:
- (1,5)
- (3,3)
- (5,1)
These represent the different combinations of rolling the dice and getting numbers that add up to an odd number. There are a total of 3 favorable outcomes.
Using the same logic as above, the total number of possible outcomes is still 6 * 6 = 36.
P(sum is an odd number) = 3/36 = 1/12
This can be simplified to approximately 0.0833 or 8.33% chance of rolling a sum that is an odd number.