A pair of dice is rolled.What is the probability that the sum of the pips is either an even number on a multiple of 3?
total number of space is 36.
Sum even = 2, 4, 6, 8, 10, 12
Mult. of 3 = 3, 6, 9, 12
Note that 6 and 12 fit both criteria.
Either-or probabilities are found by adding the individual probabilities.
1200/ 1296
To find the probability of getting a sum of pips that is either an even number or a multiple of 3 when rolling a pair of dice, we need to determine the number of favorable outcomes and divided it by the total number of possible outcomes.
Let's first find the favorable outcomes:
- Even numbers: The possible even sums from rolling two dice are 2, 4, 6, 8, 10, and 12. Out of these, there are 3 even numbers: 4, 6, and 8.
- Multiples of 3: The possible sums that are multiples of 3 are 3, 6, 9, and 12. Out of these, there are 2 multiples of 3: 6 and 12.
Therefore, the total number of favorable outcomes is 3 + 2 = 5.
Now, let's find the total number of possible outcomes:
When rolling two dice, each dice has 6 possible outcomes (numbers 1 through 6). Therefore, the total number of possible outcomes is 6 * 6 = 36.
Finally, we can find the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes
Probability = 5 / 36
Therefore, the probability of getting a sum of pips that is either an even number or a multiple of 3 when rolling a pair of dice is 5/36.
To find the probability that the sum of the pips is either an even number or a multiple of 3, we need to determine the number of outcomes that satisfy this condition and divide it by the total number of possible outcomes.
Let's analyze the requirements:
1. The sum of the pips is an even number:
There are several possible outcomes for an even sum of pips: (1,1), (1,3), (1,5), (1,6), (2,2), (2,4), (2,6), (3,3), (3,5), (3,6), (4,4), (4,6), (5,5), (5,6), and (6,6). That makes a total of 15 outcomes.
2. The sum of the pips is a multiple of 3:
There are several possible outcomes for a sum of pips that is a multiple of 3: (1,2), (1,5), (2,1), (2,4), (3,3), (4,2), (4,5), (5,1), (5,4), and (6,3). This gives us a total of 10 outcomes.
However, we need to be careful not to count the outcomes that satisfy both conditions twice. Luckily, there is only one overlapping outcome, which is (3,3). Therefore, we need to subtract this double-counted outcome.
Now, we can calculate the probability by dividing the total number of desired outcomes by the total number of possible outcomes:
Desired outcomes = 15 + 10 - 1 = 24
Total possible outcomes = 36
Probability = Desired outcomes / Total possible outcomes
Probability = 24 / 36
Probability = 2 / 3
So, the probability that the sum of the pips is either an even number or a multiple of 3 is 2/3.