Cassie rolled two 1-6 cubes 108 times. How many times should she predict the sum of 5?
To find out how many times Cassie should predict the sum of 5 when rolling two 1-6 cubes 108 times, we need to calculate the probability of rolling a sum of 5 in one roll and then multiply it by 108.
There are a total of 11 possible outcomes when rolling two 1-6 cubes:
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
Out of those 11 possible outcomes, there is only one way to roll a sum of 5 (i.e., rolling a 1 on one die and a 4 on the other, or rolling a 2 on one die and a 3 on the other).
So, the probability of rolling a sum of 5 in one roll is 1/11.
To find out how many times Cassie should predict the sum of 5 in 108 rolls, we multiply the probability of rolling a sum of 5 by 108:
1/11 * 108 = 9.8182
Since we cannot have a fraction of a roll, Cassie should predict it to occur 9 times.
To find out how many times Cassie should predict the sum of 5 when rolling two 1-6 cubes 108 times, we need to understand the probability of getting a sum of 5 on each roll.
When rolling two dice, each die can have 6 possible outcomes (numbers 1-6). So, the total number of outcomes when rolling two dice is 6 multiplied by 6, which is 36.
To determine the number of outcomes that result in a sum of 5, we can list all the possibilities:
- (1, 4)
- (2, 3)
- (3, 2)
- (4, 1)
There are 4 possible outcomes that yield a sum of 5.
To calculate the probability of getting a sum of 5, we divide the number of favorable outcomes (4) by the total number of outcomes (36):
Probability = Number of favorable outcomes / Total number of outcomes = 4/36 = 1/9
Now, to predict how many times Cassie should expect the sum of 5 when rolling two dice 108 times, we multiply the probability (1/9) by the total number of rolls (108):
Expected frequency = Probability * Total number of rolls = (1/9) * 108 = 12
Therefore, Cassie should predict the sum of 5 around 12 times when rolling two 1-6 cubes 108 times, based on the probability calculation.
sum of 5:
14, 23, 32, 41 ----- 4 cases:
prob(5 with 2 dice) = 4/36 = 1/9
number of times for 108 rolls
= (1/9)(108) = 12