To solve this problem, we need to determine the probability of the sum of outcomes on the top faces of two rolled dice being either 7 or 10.
First, let's consider the total number of possible outcomes when two dice are rolled. Each die has 6 faces, which results in a total of 6 \times 6 = 36 possible outcomes.
Next, we'll find the number of outcomes where the sum is 7. These combinations are:
- (1, 6)
- (2, 5)
- (3, 4)
- (4, 3)
- (5, 2)
- (6, 1)
There are 6 outcomes where the sum is 7.
Now, let's find the number of outcomes where the sum is 10. These combinations are:
- (4, 6)
- (5, 5)
- (6, 4)
There are 3 outcomes where the sum is 10.
To find the probability of the sum being either 7 or 10, we add the favorable outcomes:
The total number of favorable outcomes = 6 (sum = 7) + 3 (sum = 10) = 9.
The probability is therefore given by dividing the number of favorable outcomes by the total number of possible outcomes:
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{9}{36} = \frac{1}{4} = 0.25
The correct answer is 0.25, which corresponds to the given option.
Important Questions from Probability
Two dice are thrown simultaneously. What is the probability of getting the same number on both the dice?
The probability of being 53 Sundays in year 2020 is-
Three dice are thrown randomly. The probability of coming 3 in at least one die is
The probability of having 53 Tuesdays in an ordinary year is:
When two dice are tossed simultaneously, the probability that the sum of the numbers appearing on both the dice is 8 will be
