What is the probability that a 10-sided die is rolled 3 times and each time the value was unique (i.e. there are no repeating values from previous rolls)?
I know I can do this with a tree diagram fairly easily, but is there a formula for it that doesn't involve one of those? They're time-consuming.
On the first roll, there are 10 possible outcomes.
For the second roll you want it to be different from the first, so only 9 possible outcomes, with 8 as the third
So the prob(your event) = 10*9/8/1000
= .72
Ah awesome! Any specific reason we're dividing by 1000? Just to get the right decimal?
Multiplication rule:
(10/10)*(9/10)*(8/10)=10*9/8/1000
To find the probability that a 10-sided die is rolled 3 times and each time the value is unique, we can use the concept of permutations.
Let's break down the problem step by step:
Step 1: Find the total number of possible outcomes.
Since we are rolling a 10-sided die 3 times, each roll has 10 possible outcomes. So the total number of possible outcomes is 10 * 10 * 10 = 1000.
Step 2: Find the number of favorable outcomes.
In the first roll, we have 10 possible outcomes. In the second roll, we have 9 possible outcomes since one value has already been used. Similarly, in the third roll, we have 8 possible outcomes since two values have already been used.
So the number of favorable outcomes is 10 * 9 * 8 = 720.
Step 3: Calculate the probability.
The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
So the probability = 720/1000 = 0.72 or 72%.
So, in this case, the probability that a 10-sided die is rolled 3 times and each time the value was unique is 0.72 or 72%.
While a tree diagram can indeed help visualize the problem, it is not always necessary to use one. In this case, recognizing the concept of permutations allows us to solve the problem without needing a tree diagram.