There is an octahedral (8-faces) die whose faces each have one different number from the set {1, 2, 3, 4, 5, 6, 7, 8}. The die is rolled twice, and the number appearing on top after the first roll is multiplied by the number appearing on top after the second roll. What is the probability that this product is divisible by 9?
It can only be divisible by 9 if the number on each roll is divisible by 3, i.e. is 3 or 6. There is a2/8 chance of this on each roll so the probability is 2/8 x 2/8 = 1/16.
Getting a number from rolling an octahedral (8-sided) die.
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To find the probability that the product of two rolls is divisible by 9, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Let's start by considering the possible outcomes.
Since the die has 8 faces numbered from 1 to 8, the total number of possible outcomes for the first roll is 8.
Similarly, for the second roll, we have 8 possible outcomes again.
Therefore, the total number of possible outcomes for both rolls is 8 * 8 = 64.
Now, let's determine the favorable outcomes – the combinations of numbers that lead to a product divisible by 9.
For a product to be divisible by 9, at least one of the rolls must be divisible by 9. Let's analyze the possibilities:
1. If the first roll is divisible by 9 (i.e., 9), then any number from 1 to 8 can appear on the second roll. So there are 8 favorable outcomes for this case.
2. If the second roll is divisible by 9 (i.e., 9), then any number from 1 to 8 can appear on the first roll. Again, there are 8 favorable outcomes for this case.
3. If both rolls are divisible by 9 (i.e., 9), then there is only one favorable outcome for this case.
Therefore, the total number of favorable outcomes is 8 + 8 + 1 = 17.
Now that we know the total number of possible outcomes (64) and the total number of favorable outcomes (17), we can calculate the probability.
The probability of an event is given by the number of favorable outcomes divided by the number of possible outcomes.
So, the probability that the product of the two rolls is divisible by 9 is:
Probability = Number of Favorable Outcomes / Number of Possible Outcomes
Probability = 17 / 64
Simplifying this fraction, we get:
Probability = 0.265625
Therefore, the probability that the product is divisible by 9 is approximately 0.265625 or 26.56%.
the only rolls that are divisible by 9 are 33, 36, 63 and 66
So, 4/64 is what you get