Find the probability of obtaining a total of 4 when 4 fair dice are thrown together
To find the probability of obtaining a total of 4 when 4 fair dice are thrown together, we need to determine the number of ways we can get a sum of 4 and divide it by the total number of possible outcomes.
The possible outcomes for each dice include the numbers 1, 2, 3, 4, 5, and 6. Therefore, the total number of possible outcomes when throwing 4 dice is 6^4 = 1296 (since there are 6 possible outcomes for each dice and we are throwing 4 dice).
To determine the number of ways to obtain a sum of 4, we can use the concept of combinations. The sum of 4 can be obtained with the following combinations of numbers:
1 + 1 + 1 + 1
1 + 1 + 2
1 + 2 + 1
2 + 1 + 1
2 + 2
1 + 3
3 + 1
There are 7 different combinations that can result in a sum of 4.
Therefore, the probability of obtaining a total of 4 when throwing 4 fair dice together is 7/1296, which can be simplified to 1/186.
To find the probability of obtaining a total of 4 when 4 fair dice are thrown together, we can use the concept of combinations and probability.
Step 1: Determine the number of possible outcomes.
When throwing a fair die, there are 6 possible outcomes (numbers 1 to 6) on each die. Since we are throwing 4 dice together, the total number of possible outcomes is 6 multiplied by itself 4 times, also known as 6^4.
Total number of outcomes = 6^4 = 1,296.
Step 2: Determine the number of favorable outcomes.
To obtain a total of 4, we need to identify the combinations of numbers that add up to 4 when the 4 dice are thrown. The possible combinations are:
1+1+1+1
1+1+2
1+2+1
2+1+1
1+3
3+1
2+2
There are 7 favorable outcomes that add up to 4 when throwing 4 dice.
Step 3: Compute the probability.
The probability of obtaining a total of 4 when throwing 4 fair dice is given by:
Probability = (Number of Favorable Outcomes) / (Total Number of Outcomes)
= 7 / 1,296
≈ 0.0054
Therefore, the probability of obtaining a total of 4 when throwing 4 fair dice together is approximately 0.0054, or 0.54%.