Answer:
16.7% probability that you will roll doubles.
8.3% probability that you will roll a sum of four.
Theoretical probabilities;
Step-by-step explanation:
These are all the possible outcomes:
(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)
(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)
(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)
(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)
(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)
(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)
There are 36 possible outcomes
What is the probability that you will roll doubles?
There are 6 outcomes that are doubles. (1,1),(2,2),(3,3),(4,4),(5,5),(6,6)
So there is a 6/36 = 1/6 = 0.166 = 16.7% probability that you will roll doubles.
What is the probability that you will roll a sum of four?
There are 3 outcomes with a sum of four: (1,3), (2,2), (3,1)
So there is a 3/36 = 0.083 = 8.3% probability that you will roll a sum of four.
Are these empirical or a theoretical probabilities?
Empirical probability is about the observed counts, it is calculated after the dice has been thrown.
Theoretical are the expected probabilities, calculated before the event happens. In this case, these are theoretical probabilities.
The probabilities are theoretical probabilities
The probability of rolling double
In a roll of two dice, there are 6 outcomes of a double out of a total of 36 outcomes
So, the probability of rolling double is:
p = 6/36
Simplify
p = 1/6
Hence, the probability of rolling a double is 1/6
The probability of rolling a sum of 4
In a roll of two dice, there are 3 outcomes of a sum of 4 out of a total of 36 outcomes
So, the probability of rolling a sum of 4 is:
p = 3/36
Simplify
p = 1/12
Hence, the probability of rolling a sum of 4 is 1/12
The probabilities are theoretical probabilities because they actual results may not reflect the calculated value
Read more about probabilities at:
https://brainly.com/question/25870256
