) What is the theoretical probability of rolling a sum of nine with two standard six-sided dice?
d) Ted wanted to compare theoretical probablity to experimental probability. He rolled two standard 6 sided dice 50 times, and got a sum of nine a total of 11 times. Calculate the experimental probability of rolling a sum of nine with two standard dice
e) If the dice were rolled 1200 times, how many times do you think a sum of nine would be rolled?
a) The theoretical probability of rolling a sum of nine with two standard six-sided dice can be calculated by finding the number of ways to get a sum of nine (which is four: (3,6), (4,5), (5,4), (6,3)) and dividing it by the total number of possible outcomes (36):
Theoretical Probability = Number of favorable outcomes / Total number of outcomes
Theoretical Probability = 4/36
Theoretical Probability = 1/9
b) Experimental Probability:
Experimental Probability = Number of times event occurred / Total number of experiments
Experimental Probability = 11/50
c) If the dice were rolled 1200 times, we can use the experimental probability calculated in part b) to estimate the number of times a sum of nine would be rolled:
Expected number of times a sum of nine would be rolled = Experimental Probability * Total number of experiments
Expected number of times a sum of nine would be rolled = 11/50 * 1200
Expected number of times a sum of nine would be rolled = 264
Therefore, if the dice were rolled 1200 times, it is expected that a sum of nine would be rolled approximately 264 times.