The probability of getting a sum of 5 when you roll two number cubes
is How many times should you expect to get a sum of 5 if you roll
the cubes each number of times?
a. 9 b. 18 c. 27 d. 100 e. 450
--- 1 2 3 4 5 6
1========1,4
2 =====2,3
3 ==3,2
4=4,1
5
6
four out of 36 = 1/9
that is one out of every nine
so
a once
b twice
c three times
d 100/9 = about 11 times
e 450/9 = 50 times
To find the probability of getting a sum of 5 when rolling two number cubes, we need to determine the number of ways we can get a sum of 5 divided by the total number of possible outcomes.
First, let's list all the possible outcomes when rolling two number cubes. Each cube has 6 sides numbered 1 to 6, so there are 6 * 6 = 36 possible outcomes in total.
We can get a sum of 5 when rolling the two cubes in the following ways:
- (1, 4)
- (2, 3)
- (3, 2)
- (4, 1)
So, there are four ways to get a sum of 5.
The probability can now be calculated by dividing the number of favorable outcomes (4) by the total number of possible outcomes (36):
Probability = 4/36 = 1/9
Now, let's consider the question of how many times we can expect to get a sum of 5 if we roll the cubes each number of times.
To find the expected number of times, we multiply the probability by the total number of rolls.
Let's calculate the expected number of times for each option:
a. 9: Expected number of times = (1/9) * 9 = 1
b. 18: Expected number of times = (1/9) * 18 = 2
c. 27: Expected number of times = (1/9) * 27 = 3
d. 100: Expected number of times = (1/9) * 100 ≈ 11.1
e. 450: Expected number of times = (1/9) * 450 ≈ 50
So, if you roll the cubes each number of times, you would expect to get a sum of 5 approximately:
- 1 time if you roll 9 times
- 2 times if you roll 18 times
- 3 times if you roll 27 times
- 11 times if you roll 100 times
- 50 times if you roll 450 times
Therefore, the answer is (b) 18.