A pair of dice is rolled, and a number that appears uppermost on each die is observed, Refer to this experiment and find the probability of the given event. (Enter your answer as a fraction)The sume of the numbers ia an add number.
Would it not make logical sense that half the sums would be even and half would be odd ?
e.g.
1,1 -- even
1,2 --odd
1,3 -- even
...
6,1 -- odd
6,2 -- even
..
6,6, -- even , count them if that doesn't make sense
prob(odd sum) = 18/36 = 1/2
Why did the dice go to therapy?
Because they were looking for some common ground!
But to answer your question, let's determine the probability of getting an odd sum when rolling a pair of dice.
To find the odd sum, we need to consider all the possible combinations that result in an odd number. Here are the possible sums and their occurrences:
2 (1, 1) - odd
3 (1, 2), (2, 1) - even
4 (1, 3), (3, 1) - even
5 (1, 4), (4, 1), (2, 3), (3, 2) - odd
6 (1, 5), (5, 1), (2, 4), (4, 2), (3, 3) - even
7 (1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3) - odd
8 (2, 6), (6, 2), (3, 5), (5, 3), (4, 4) - even
9 (3, 6), (6, 3), (4, 5), (5, 4) - odd
10 (4, 6), (6, 4), (5, 5) - even
11 (5, 6), (6, 5) - odd
12 (6, 6) - even
Out of these 36 possible outcomes, there are 18 outcomes that result in an odd sum.
Therefore, the probability of rolling a pair of dice with an odd sum is 18/36, which simplifies to 1/2.
So, the probability of getting an odd sum is 1/2.
To find the probability of the sum of the numbers being an odd number when rolling a pair of dice, we need to determine the total number of outcomes and the number of favorable outcomes.
Total Number of Outcomes:
When rolling a pair of dice, each die has 6 possible outcomes (numbers 1, 2, 3, 4, 5, and 6).
Therefore, the total number of outcomes is 6 * 6 = 36.
Favorable Outcomes:
Now, let's determine the favorable outcomes, i.e., the number of outcomes where the sum of the numbers is an odd number.
There are the following possible combinations where the sum of the numbers is an odd number:
(1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (3, 6), (4, 1), (4, 3), (4, 5), (5, 2), (5, 4), (5, 6), (6, 1), (6, 3), (6, 5)
Counting these combinations, we find that there are 18 favorable outcomes.
Probability:
The probability is defined as the favorable outcomes divided by the total number of outcomes.
So, the probability of the sum of the numbers being an odd number is:
18 (favorable outcomes) / 36 (total outcomes) = 1/2
Therefore, the probability of the sum of the numbers being an odd number is 1/2.
To find the probability of the sum of the numbers rolled on a pair of dice being an odd number, we first need to count the number of favorable outcomes.
In total, there are 6 possible outcomes for each die, as there are 6 faces numbered from 1 to 6. Therefore, the total number of outcomes for the pair of dice is 6 x 6 = 36.
Next, we need to determine the favorable outcomes, i.e., the outcomes where the sum of the numbers is an odd number.
For the sum of two numbers to be odd, one number must be even while the other must be odd. There are three even numbers on each die (2, 4, 6) and three odd numbers (1, 3, 5). Therefore, the number of favorable outcomes is 3 x 3 = 9.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of outcomes:
Probability = Number of Favorable Outcomes / Total Number of Outcomes
Probability = 9 / 36
Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor, we get:
Probability = 1 / 4
Therefore, the probability of getting a sum on a pair of dice that is an odd number is 1/4.