A pair of fair dice is tossed once. Find the probability a sum of 5 or 3 appears.
The two dice are assumed to give random and independent results.
So the outcomes for each die is equally probable.
You can construct a 6x6 table containing all 36 possible outcomes, and pick out those with a sum of 3 or 5. The total number of these favourable outcomes divided by 36 gives the required probability.
You are probably familiar with combinatoric counts of the outcomes totaling 3 or 5. The count divided by 36 also gives the required probability.
jnjnj
To find the probability that a sum of 5 or 3 appears when a pair of fair dice is tossed, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
Let's first determine the total number of possible outcomes when tossing a pair of dice. Each die has 6 sides, so the total number of outcomes is 6 x 6 = 36.
Next, let's determine the number of favorable outcomes.
For a sum of 5, we can have the following combinations: (1, 4), (2, 3), (3, 2), (4, 1). So, there are 4 favorable outcomes.
For a sum of 3, we can have the following combinations: (1, 2), (2, 1). So, there are 2 favorable outcomes.
Therefore, the total number of favorable outcomes is 4 + 2 = 6.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 6 / 36
Now, we simplify the fraction:
Probability = 1 / 6
So, the probability that a sum of 5 or 3 appears when a pair of fair dice is tossed is 1/6.
To find the probability of getting a sum of 5 or 3 when tossing a pair of fair dice, we need to first determine the total number of possible outcomes and then count the number of favorable outcomes.
Step 1: Determine the total number of possible outcomes
When tossing a pair of fair dice, each die has six possible outcomes (numbers 1 to 6). Since we are tossing two dice, we need to multiply the number of outcomes for each die. So, the total number of possible outcomes is 6 x 6 = 36.
Step 2: Count the number of favorable outcomes
To find the favorable outcomes, we need to identify all the possible ways to get a sum of 5 or 3.
Sum of 5:
There are four ways to get a sum of 5: (1, 4), (4, 1), (2, 3), (3, 2).
Sum of 3:
There are two ways to get a sum of 3: (1, 2), (2, 1).
Step 3: Calculate the probability
Now that we have the count of favorable outcomes (6) and the total number of possible outcomes (36), we can calculate the probability.
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = 6 / 36
Probability = 1 / 6
Therefore, the probability of obtaining a sum of 5 or 3 when tossing a pair of fair dice is 1/6.