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 distinct natural numbers from 1 to 9 are picked at random. What is the probability that their product has 1 in its unit place?
Two dice are thrown. What is the probability that difference of numbers on them is 2 or 3 ?
Suppose that there is a chance for a newly constructed building to collapse, whether the design is faulty or not. The chance that the design is faulty is 10%. The chance that the building collapses is 95% if the design is faulty, otherwise it is 45%. If it is seen that the building has collapsed, then what is the probability that it is due to faulty design?
What is the probability that boys and girls sit alternatively?
What is the probability that P and Q take the two end positions?
