compute the probability of each of the following Event A: The sum is greater tha

Question

compute the probability of each of the following Event A: The sum is greater than 6 LEKS Gradebook Calend An ordinary (fair) die is a cube with the numbers l through 6 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 A: The sum is greater than 6 Event B. The sum is divisible by 2 or 4 (or both). Round your answers to at least two decimal places. Clear Undo He Next O Type here to search

Explanation / Answer

When this die is rolled two times, The outcomes are,

S = { (1,1), (1,2) ,...(1,6), (2,1),....(6,6)}

n(S) = 36 Number of outcomes.

Ex. We get , (1,1) then sum is 2. ( 1,2) the sum is 3, so on ( 6,6) then sum is 12.

Let A = The event that the sum is greater than 6

Then outcomes are :

A = { (1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,3),(4,4),(4,5)(4,6),(5,2),(5,3),(5,4),(5,5),(5,6)

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

n(A) = 21

By definition of probability,

P(A) = n(A)/n(S) = 21/36 = 0.5833

Similarly,

B = event that sum is divided by 2 or 4.

B={ (1,1), (1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(4,6),(5,1),(5,3),(5,5),(6,2),(6,4),(6,6)}

n(B) = 18

By definition of probability,

P(B) = n(B)/n(S) = 18/36 = 0.5

Hence, we get

P(A) = 0.5833

P(B) = 0.5

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