What is the probability of obtaining a sum of at least 4 when rolling a pair of dice?
Probability of 3 = 1+2 or 2+1 = 2/36
Probability of 2 = 1+1 = 1/36
Probability of at least 4 = 1 - 3/36 = ?
1/12
To determine the probability of obtaining a sum of at least 4 when rolling a pair of dice, we can use a combination of counting outcomes and determining favorable outcomes.
Step 1: Determine the total number of possible outcomes when rolling a pair of dice.
Since each die has 6 sides, the total number of outcomes is given by 6 multiplied by 6, which equals 36.
Step 2: Identify the favorable outcomes.
We want to find the number of outcomes that result in a sum of at least 4.
The possible sums that satisfy this condition are:
- 4 (1+3, 2+2, 3+1)
- 5 (1+4, 2+3, 3+2, 4+1)
- 6 (1+5, 2+4, 3+3, 4+2, 5+1)
- 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1)
- 8 (2+6, 3+5, 4+4, 5+3, 6+2)
- 9 (3+6, 4+5, 5+4, 6+3)
- 10 (4+6, 5+5, 6+4)
- 11 (5+6, 6+5)
- 12 (6+6)
In total, there are 9 possible favorable outcomes.
Step 3: Calculate the probability.
Finally, divide the number of favorable outcomes (9) by the total number of possible outcomes (36) to get the probability.
Probability = Favorable outcomes / Total outcomes = 9 / 36 = 1/4 = 0.25
Therefore, the probability of obtaining a sum of at least 4 when rolling a pair of dice is 0.25 or 1/4.
To find the probability of obtaining a sum of at least 4 when rolling a pair of dice, we need to determine the number of outcomes that satisfy the given condition and divide it by the total number of possible outcomes.
First, let's determine the total number of possible outcomes when rolling a pair of dice. Each die has 6 sides, so there are 6 possible outcomes for the first die and 6 possible outcomes for the second die. Therefore, the total number of outcomes is 6 x 6 = 36.
Now let's determine the number of outcomes that result in a sum of at least 4. We can calculate this by analyzing the different possible combinations:
1. For a sum of 4, we can obtain it with (1, 3), (2, 2), or (3, 1), which are 3 different outcomes.
2. For a sum of 5, we can obtain it with (1, 4), (2, 3), (3, 2), or (4, 1), which are 4 different outcomes.
3. For a sum of 6, we can obtain it with (1, 5), (2, 4), (3, 3), (4, 2), or (5, 1), which are 5 different outcomes.
4. For a sum of 7, we can obtain it with (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), or (6, 1), which are 6 different outcomes.
5. For a sum of 8, we can obtain it with (2, 6), (3, 5), (4, 4), (5, 3), or (6, 2), which are 5 different outcomes.
6. For a sum of 9, we can obtain it with (3, 6), (4, 5), (5, 4), or (6, 3), which are 4 different outcomes.
7. For a sum of 10, we can obtain it with (4, 6), (5, 5), or (6, 4), which are 3 different outcomes.
8. For a sum of 11, we can obtain it with (5, 6) or (6, 5), which are 2 different outcomes.
9. For a sum of 12, we can obtain it with (6, 6), which is 1 outcome.
Adding up the number of outcomes for each sum gives us a total of 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 33 outcomes.
Therefore, the probability of obtaining a sum of at least 4 when rolling a pair of dice is 33/36, which can also be simplified as 11/12.