if three dices are thrown simultaneously, what is the probability of having a same number on all dices and also find the probability that sum of numbers on first two dice is 10 and 12?
if three dices are thrown simultaneously, what is the probability of having a same number on all dices and also find the probability that sum of numbers on first two dice is 10 and 12?
Answer: The probability of having the same number on all three dice is equal to the probability of rolling any specific number on one die, raised to the power of three, since each die is independent.
There are 6 possible outcomes for each die, so the probability of rolling any specific number on one die is 1/6. Therefore, the probability of having the same number on all three dice is:
(1/6)^3 = 1/216
The probability of getting a sum of 10 on the first two dice can be calculated by finding all possible combinations of rolls that add up to 10. We can do this by listing out all the possible outcomes for the first two dice:
(1, 9), (2, 8), (3, 7), (4, 6), (5, 5), (6, 4), (7, 3), (8, 2), (9, 1)
There are 9 possible outcomes, and each outcome has a probability of 1/36, since there are 36 possible outcomes for two dice. Therefore, the probability of getting a sum of 10 on the first two dice is:
9/36 = 1/4
Similarly, the probability of getting a sum of 12 on the first two dice can be calculated by listing out all possible outcomes:
(1, 11), (2, 10), (3, 9), (4, 8), (5, 7), (6, 6), (7, 5), (8, 4), (9, 3), (10, 2), (11, 1)
There are 11 possible outcomes, each with a probability of 1/36. Therefore, the probability of getting a sum of 12 on the first two dice is:
11/36