Question

DATA ANALYSIS AND STATISTICSProbabilities involving two rolls of a dieAn ordinary (falr) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in successionand that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.Compute the probability of each of the following events.Event A: The sum is greater than 8.Event B: The sum is divisible by 4.Write your answers as fractions.

Answer 1

To give all possible results, this is the sample space of the distribution ;

Event A, the sum is greater than 8.

The total possible outcomes is 36.

The sum being greater than 8 happens 10 times.

Therefore, the probability that the sum is greater than 8 is;

`\begin{gathered} \\ (10)/(36)=(5)/(18) \end{gathered}`

Event B, The sum is dividible by 4.

In the sample space, there are 9 places where the sum is divisible by 4.

Therefore, the probability that the sum is divisible by 4 is;

`(9)/(36)=(1)/(4)`