Two 4-sided dice are rolled and the sum is recorded. Determine the theoretical probability of rolling a sum of 6.
Hint: You may want to create a dice chart for the sum of two 4-sided die.
a. 3/16
b. 6/16
c. 2/16
d. 4/16
There are 16 possible rolls
How many come up 6? 24, 42
So, P(sum=6) = 2/16
Well, rolling two 4-sided dice is like throwing a party with very few possibilities. Let's see what we get on our dice chart.
To roll a sum of 6, we can have two outcomes: (1, 5) and (2, 4).
So, out of the 16 possible outcomes (4 x 4), we have 2 ways to get a sum of 6.
Therefore, the theoretical probability of rolling a sum of 6 is 2/16.
But hey, let's reduce that fraction to the simplest form. 2/16 is the same as 1/8.
So the correct answer is 1/8, which I'm afraid none of the options you provided. But you're welcome for the laugh! 🤡
To determine the theoretical probability of rolling a sum of 6 with two 4-sided dice, we can create a dice chart to visualize all the possible outcomes.
When rolling two 4-sided dice, each die has the numbers 1, 2, 3, and 4.
The chart for the sum of two 4-sided dice will look like this:
| Die 1 | Die 2 | Sum |
|-------|-------|-----|
| 1 | 1 | 2 |
| 1 | 2 | 3 |
| 1 | 3 | 4 |
| 1 | 4 | 5 |
| 2 | 1 | 3 |
| 2 | 2 | 4 |
| 2 | 3 | 5 |
| 2 | 4 | 6 |
| 3 | 1 | 4 |
| 3 | 2 | 5 |
| 3 | 3 | 6 |
| 3 | 4 | 7 |
| 4 | 1 | 5 |
| 4 | 2 | 6 |
| 4 | 3 | 7 |
| 4 | 4 | 8 |
Out of the 16 possible outcomes, there are 2 outcomes where the sum is 6: (2, 4) and (3, 3).
Therefore, the theoretical probability of rolling a sum of 6 is 2/16.
So, the correct choice is c. 2/16.
To determine the theoretical probability of rolling a sum of 6 with two 4-sided dice, you need to consider all the possible outcomes.
To create a dice chart, list all the possible outcomes for each die and their corresponding sums. For a 4-sided die, the possible outcomes are 1, 2, 3, and 4. Write these outcomes in a table, with one die's outcomes listed as row headings and the other die's outcomes listed as column headings. Then fill in each cell with the sum of the corresponding row and column headings.
Here is an example of a dice chart for two 4-sided dice:
| 1 | 2 | 3 | 4 |
-------------------------------
1 | 2 | 3 | 4 | 5 |
-------------------------------
2 | 3 | 4 | 5 | 6 |
-------------------------------
3 | 4 | 5 | 6 | 7 |
-------------------------------
4 | 5 | 6 | 7 | 8 |
Now, count the number of outcomes that yield a sum of 6. In this case, there are 2 outcomes: (1, 5) and (2, 4).
The total number of possible outcomes is the total number of cells in the chart, which is 4 x 4 = 16.
So, the theoretical probability of rolling a sum of 6 is 2/16.
Therefore, the correct answer is option c. 2/16.