A pair of dice with faces numbered 1,2,3,4,5 and 6 is rolled once.what is the probability of obtaining at least a sum of 6
To find the probability of obtaining at least a sum of 6 when rolling a pair of dice, we need to count the number of favorable outcomes and divide it by the total number of possible outcomes.
Total number of outcomes when rolling two dice: 6 * 6 = 36
To find the favorable outcomes, we can list all the possible outcomes that satisfy the condition:
1 + 5 = 6 (favorable)
2 + 4 = 6 (favorable)
3 + 3 = 6 (favorable)
4 + 2 = 6 (favorable)
5 + 1 = 6 (favorable)
6 + 6 = 12 (not favorable)
There are 5 favorable outcomes and 1 unfavorable outcome.
Therefore, the probability of obtaining at least a sum of 6 is:
P(at least a sum of 6) = favorable outcomes / total outcomes
P(at least a sum of 6) = 5 / 36
So, the probability of obtaining at least a sum of 6 when rolling a pair of dice is 5/36.
To find the probability of obtaining at least a sum of 6 when rolling a pair of dice, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.
Let's start by listing all the possible outcomes when rolling a pair of dice:
Possible outcomes: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
Out of these 36 possible outcomes, we need to calculate the number of favorable outcomes, i.e., the pairs of numbers that give a sum of 6 or greater. We can count these outcomes:
Favorable outcomes: (1,5), (1,6), (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
There are 26 favorable outcomes.
Now, we can calculate the probability of obtaining at least a sum of 6 by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
P(at least a sum of 6) = 26/36
Simplifying the fraction, we get:
P(at least a sum of 6) = 13/18
Therefore, the probability of obtaining at least a sum of 6 when rolling a pair of dice is 13/18.