Eben rolls two standard number cubes 36 times. Predict how many times he will roll a sum of 4.
To predict the number of times Eben will roll a sum of 4 when rolling two standard number cubes 36 times, we need to understand the probabilities involved.
A standard number cube has six faces, numbered from 1 to 6. When rolling two dice, each die has a total of six possible outcomes, resulting in a total of 6 x 6 = 36 possible combinations.
To find the probability of rolling a sum of 4 on two number cubes, we need to determine how many of the 36 possible combinations yield a sum of 4.
The possible combinations that give us a sum of 4 are (1, 3), (3, 1), (2, 2).
So, out of the 36 possible combinations, 3 of them give us a sum of 4.
To predict the number of times Eben will roll a sum of 4, we can use the concept of probability. The probability of rolling a sum of 4 is the number of favorable outcomes (3) divided by the number of total outcomes (36).
Probability of rolling a sum of 4 = (Number of favorable outcomes) / (Number of total outcomes)
Probability of rolling a sum of 4 = 3 / 36
Simplifying the above expression, we get:
Probability of rolling a sum of 4 = 1 / 12
Now, to predict the number of times Eben will roll a sum of 4 in 36 attempts, we can multiply the probability by the number of trials:
Number of times Eben will roll a sum of 4 = (Probability of rolling a sum of 4) x (Number of trials)
Number of times Eben will roll a sum of 4 = (1 / 12) x 36
Number of times Eben will roll a sum of 4 = 3
Therefore, based on the probability calculations, we can predict that Eben will roll a sum of 4 approximately 3 times when rolling the two standard number cubes 36 times.