Compute the probability of each of the following events Roun

Compute the probability of each of the following events:

Round your answers to at least two decimal places.

P(A)=

P(B)=

An ordinary (fair) die is a cube with the numbers through on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and 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 : The sum is greater than . Event : The sum is not divisible by . Round your answers to at least two decimal places. P(A)= P(B)=

Solution

When you have a two-dice problem you should draw it. The sample space is  6x6 rectangle listing all the

possible sums you might get as a result of tossing the two dices together.

Lets first see the possible outcomes for the situation:

Event A: Sum is greater than 5:

(1,5), (1,6),(2,4),(2,5),(2,6),(3,3),(3,4), (3,5),(3,6),(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 26 such cases where the sum will be greater than 5

Therefore,

P(A) = 26/36 = 0.72222= 0.72

Event B: The sum is not divisible by 5

Lets check which of the possible sums are divisible by 6

(1,4), (2,3), (3,2), (4,1), (4,6), (5,5), (6,4)

There are 7 such cases out of 36 which are divisible by 5. So probability of getting a sum which is divisible by 5 is 7/36

Therefore, the probability of getting a sum which is not divisible by 5; P(B) =1- 7/36

P(B) = 29/36 = 0.805555 = 0.81