Can someone please help me understand this. This is not graded or anything I just want to know how to do this.
- Chloe rolls two-sided number cubes and adds the numbers showing on the cubes. What is the probability that the sum of the number cubes is even or five?
just count the ways the event can happen
even:
11 13 15
22 24 26
31 33 35
42 44 46
51 53 55
62 64 66
So, there are 18 ways to roll an even.
There are 4 ways to get a five: 14 23 32 41
So, P(even or 5) = 20/36
To find the probability of rolling an even sum or a sum of five using two-sided number cubes, we need to first determine the total number of possible outcomes.
Each number cube has two sides, so there are 2 possibilities for the first cube and 2 possibilities for the second cube. The total number of outcomes is then calculated by multiplying the possibilities together:
Total number of outcomes = 2 (possibilities for the first cube) * 2 (possibilities for the second cube) = 4
Next, we need to determine the number of favorable outcomes, which are the outcomes that meet our criterion of having an even sum or a sum of five.
Firstly, let's consider the even sum. For the sum to be even, we can either have two even numbers (both cubes show even numbers) or two odd numbers (both cubes show odd numbers).
The possible outcomes for an even sum are:
- (even, even)
- (odd, odd)
Next, let's consider the sum of five. There are a few possible combinations of numbers that can add up to five:
- (1, 4)
- (2, 3)
- (3, 2)
- (4, 1)
So, the possible outcomes for a sum of five are:
- (1, 4)
- (2, 3)
- (3, 2)
- (4, 1)
Now, we need to calculate the total number of favorable outcomes by adding up the possibilities from both cases:
Total number of favorable outcomes = 2 (possible outcomes for even sum) + 4 (possible outcomes for sum of five) = 6
Lastly, we calculate the probability by dividing the number of favorable outcomes by the total number of outcomes:
Probability = Number of favorable outcomes / Total number of outcomes = 6 / 4 = 1.5
However, probabilities cannot be greater than 1, so in this case, the probability is 1 (or 100%).
Therefore, the probability that the sum of the number cubes is even or five is 1 (or 100%).