Compute the probability of each of the following events: P A = P B = An ordinary

Question

Compute the probability of each of the following events:

PA

=

PB

=

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 divisible by or (or both).

Round your answers to at least two decimal places.

Explanation / Answer

Sample space = {(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)}               

a.
n(A) = sum greater than eight = { (3,6), (4,5), (4,6), (5,4),(5,5),(5,6), (6,3),(6,4),(6,5),(6,6) } = 10
P(A) = n(A)/n(S) = 10/36 = 0.2778
b.
sum is divisible by 5 = {(1,4),(2,3),(3,2),(4,1)(5,5)(6,4)(4,6)} = 7
sum is divisible by 6 = { (1,5) (2,4) (3,3) (4,2) (5,1) , (6,6) } = 6
sum is divisble by 5 and 6 = { (1,4),(2,3),(3,2),(4,1)(5,5)(6,4)(4,6) (1,5) (2,4) (3,3) (4,2) (5,1) , (6,6) } = 13
P(B) = n( 5 or 6)/ n(S) = 13/36 = 0.361111

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