What are the possible outcomes when a die is rolled once?
For example, when a die is rolled, the possible outcomes are 1, 2, 3, 4, 5, and 6. In mathematical language, an event is a set of outcomes, which describe what outcomes correspond to the “event” happening. For instance, “rolling an even number” is an event that corresponds to the set of outcomes {2, 4, 6}.
How many outcomes will you get if you toss a coin once and roll a die twice?
Explanation: When you flip a coin there are two possible outcomes (heads or tails) and when you roll a die there are six outcomes(1 to 6). Putting these together means you have a total of 2×6=12 outcomes.
How many outcomes does rolling a die have?
Note that there are 36 possibilities for (a,b). This total number of possibilities can be obtained from the multiplication principle: there are 6 possibilities for a, and for each outcome for a, there are 6 possibilities for b. So, the total number of joint outcomes (a,b) is 6 times 6 which is 36.
When a die is rolled twice how many outcomes?
36
Solution: Total number of outcomes when die is thrown twice = 6 × 6 = 36.
How many outcomes are in the event of rolling a 2 each of the 3 times?
For each of the three choices there are 2 different outcomes. The total number of outcomes is \begin{align*}2 \times 2 \times 2 = 8\end{align*}. This method of calculating the number of total outcomes can be stated as a general rule called the Counting Principle.
How many different outcomes are possible for 3 rolls of a die?
216 outcomes
Just as one die has six outcomes and two dice have 62 = 36 outcomes, the probability experiment of rolling three dice has 63 = 216 outcomes.
When you roll a die thrice how many possible outcomes are there?
Just as one die has six outcomes and two dice have 62 = 36 outcomes, the probability experiment of rolling three dice has 63 = 216 outcomes. This idea generalizes further for more dice.
When you toss a coin thrice how many possible outcomes?
If we toss three coins, we have a total of 2 × 2 × 2 = 8 possible outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT, as shown in Figure 6.4 b.
How many outcomes are possible with 3 dice?
216 possible outcomes
We can list all possible outcomes for the three dice and add a fourth column that contains a 0 if the event is not in A and contains a 1 if the event is in A. By simple counting, we find that there are 15 outcomes in event A, out of the total of 216 possible outcomes.
What is the probability of rolling a 3 twice?
The probability of rolling a specific number twice in a row is indeed 1/36, because you have a 1/6 chance of getting that number on each of two rolls (1/6 x 1/6).
What is the probability of rolling 2 dice?
Two (6-sided) dice roll probability table
| Roll a… | Probability |
|---|---|
| 2 | 1/36 (2.778\%) |
| 3 | 2/36 (5.556\%) |
| 4 | 3/36 (8.333\%) |
| 5 | 4/36 (11.111\%) |
What is the probability of rolling a 2 on a dice 3 times?
Two (6-sided) dice roll probability table
| Roll a… | Probability |
|---|---|
| 2 | 1/36 (2.778\%) |
| 3 | 3/36 (8.333\%) |
| 4 | 6/36 (16.667\%) |
| 5 | 10/36 (27.778\%) |
What is the expected number of rolls for one die?
It’s not hard to write down the expected number of rolls for a single die. You need one roll to see the first face. After that, the probability of rolling a different number is 5/6. Therefore, on average, you expect the second face after 6/5 rolls.
What does it mean to roll a die?
To dice something means to cut it into cubes, making it a similar shape to the 6-sided die we are all familiar with. To roll a die did first appear later. Dice with other numbers of sides are available, but the 6-sided die is the one we know best. Most often when playing games, each side of the die represents a different value.
How many possible outcomes are there if you roll 6 dice?
We multiply and see that there are 6 x 6 x 6 = 216 possible outcomes. As it gets cumbersome to write the repeated multiplication, we can use exponents to simplify work. For two dice, there are 6 2 possible outcomes. For three dice, there are 6 3 possible outcomes. In general, if we roll n dice, then there are a total of 6 n possible outcomes.
How do you calculate the mean time required to roll every number?
Furthermore, the mean time it takes for multiple results to appear is the sum of the mean times for each individual result to occur. This allows us to calculate the mean time required to roll every number: t = 1 / 1 + 6 / 5 + 6 / 4 + 6 / 3 + 6 / 2 + 6 / 1 = 1 + 12 / 10 + 15 / 10 + 2 + 3 + 6 = 12 + 27 / 10 = 14.7