A fair die is rolled three times. Find the chance that three different faces appear.
on the first roll, some face appears.
On the 2nd roll, there's a 5/6 chance that a new face appears
On the 3rd roll, there's a 4/6 chance that a new face appears.
So, p=(1)(5/6)(4/6) = 5/9
To find the probability that three different faces appear when rolling a fair die three times, we need to find the number of favorable outcomes and the total number of outcomes.
First, let's determine the total number of outcomes. Since we are rolling a fair die three times, the number of outcomes for each roll is 6 (since there are 6 possible outcomes for each roll). Therefore, the total number of outcomes for all three rolls is 6 * 6 * 6 = 216.
Next, let's determine the number of favorable outcomes where three different faces appear. For the first roll, we can choose any face out of the 6 faces on the die. For the second roll, there are 5 remaining faces to choose from since we want three different faces. And for the third roll, there are 4 remaining faces to choose from. Therefore, the number of favorable outcomes is 6 * 5 * 4 = 120.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of outcomes: 120 / 216 ≈ 0.556.
So, the chance that three different faces appear when rolling a fair die three times is approximately 0.556, or 55.6%.
Remember that in similar situations, you can use the concept of permutations to calculate the number of favorable outcomes and total outcomes when dealing with different arrangements or orderings.