A six sided die is rolled three times. List possible outcomes and find the probability of rolling exactly one 6.
Are you sure that they want you to "list" all the outcomes?
There are 216 of them. (6x6x6=216)
If you have to list them, do it systematically, e.g.
1 1 6
1 1 5
...
1 1 1
1 2 6
1 2 5
....
1 2 1
1 3 6
.....
....
1 6 1
...
2 1 6
2 1 5
etc
To have only one 6, it must look like this
6 x y, x 6 y, x y 6, where the x and y are NOT 6
number of those = 3x5x5 = 75
prob (exactly one 6) = 75/216 = 25/72
brah that worng
help me pls
To list the possible outcomes of rolling a six-sided die three times, we need to consider all the combinations of numbers that can appear on the die.
Each roll of the die has six possible outcomes, numbered from 1 to 6. Therefore, the total number of possible outcomes when rolling the die three times is 6^3 (since each roll is independent).
To find the probability of rolling exactly one 6 in three rolls, we need to determine the number of favorable outcomes (rolling exactly one 6) and divide it by the total number of possible outcomes.
To roll exactly one 6, we have three cases to consider:
1) The first roll is a 6, and the remaining two rolls are not 6.
2) The second roll is a 6, and the first and third rolls are not 6.
3) The third roll is a 6, and the first and second rolls are not 6.
For each case, the probability of rolling a 6 on one specific roll is 1/6, and the probability of not rolling a 6 on one specific roll is 5/6. We can use these probabilities to calculate the probability of each case.
1) The probability of rolling a 6 on the first roll is 1/6, and the probability of not rolling a 6 on the second and third rolls is (5/6)^2. Therefore, the probability of this case is (1/6) * (5/6)^2.
2) The probability of rolling a 6 on the second roll is 1/6, and the probability of not rolling a 6 on the first and third rolls is (5/6)^2. Therefore, the probability of this case is (1/6) * (5/6)^2.
3) The probability of rolling a 6 on the third roll is 1/6, and the probability of not rolling a 6 on the first and second rolls is (5/6)^2. Therefore, the probability of this case is (1/6) * (5/6)^2.
To find the total probability of rolling exactly one 6, we can sum up the probabilities of the three cases. So the probability of rolling exactly one 6 in three rolls is:
(1/6) * (5/6)^2 + (1/6) * (5/6)^2 + (1/6) * (5/6)^2 = (3/6) * (5/6)^2 = (3/6) * (25/36) = 75/216 = 25/72.
Therefore, the probability of rolling exactly one 6 is 25/72.