When two fair six-sided dice are rolled, there are 36 possible outcomes. Find the probability that either doubles are rolled or the sum of the two dice is 8.
doubles --- 6 of them
sumof 8 --- 26,35,44,53 62
total = 10 (we have to count 44 only once)
prob = 10/36 = 5/18
If three fair dice are rolled, find the probability that the sum of upturned faces is 10
When two 6-sided dice are rolled, there are 36 possible
Find the probability that the sum is not 4?
To find the probability, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Let's first calculate the number of favorable outcomes. In this case, we have two mutually exclusive favorable events:
1. Doubles are rolled: There are six possible doubles (i.e., 1-1, 2-2, 3-3, 4-4, 5-5, 6-6).
2. The sum of the two dice is 8: We can get a sum of 8 in several ways: (2-6, 3-5, 4-4, 5-3, 6-2). There are five possible outcomes.
Now, let's calculate the total number of possible outcomes. Since we have two six-sided dice, the total number of outcomes for each die is 6. Multiplying the outcomes of two dice together gives us 6 x 6 = 36 possible outcomes.
So, the number of favorable outcomes is 6 + 5 = 11, and the total number of possible outcomes is 36.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes = 11 / 36.
Therefore, the probability that either doubles are rolled or the sum of the two dice is 8 is 11/36, or approximately 0.3056.