A pair of dice is rolled. What is the probability of the sum of the numbers shown uppermost is less than 6?
10/36
5/18
(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)=6/36=1/6=0.167
To determine the probability of the sum of the numbers shown on a pair of dice being less than 6, we need to find the number of favorable outcomes and divide it by the total number of possible outcomes.
Step 1: Find the favorable outcomes
To find the favorable outcomes, we need to identify the combinations of numbers on two dice that will result in a sum less than 6. These combinations are: (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1), and (3, 1). So, there are 7 favorable outcomes.
Step 2: Find the total number of possible outcomes
To find the total number of possible outcomes, we need to calculate the number of ways we can roll two dice. Since each die has six sides, there are 6 possible outcomes for the first die and 6 possible outcomes for the second die. Therefore, the total number of possible outcomes is 6 x 6 = 36.
Step 3: Calculate the probability
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the probability is 7/36.
So, the probability of rolling a sum less than 6 on a pair of dice is 7/36.