Answer:
The probability that the sum of the two rolls is 5 is 0.455.
Step-by-step explanation:
The outcomes of the roll of two dice are:
S = {(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)}
The sum of the two numbers are in the set:
S₁ = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} = 11 possible outcomes
The subset of prime numbers from the above set is,
S₂ = {2, 3, 5, 7, 11} = 5 possible outcomes.
Compute the probability that the sum of the two rolls is 5 as follows:
[tex]P(Sum=5)=\frac{5}{11}=0.455[/tex]
Thus, the probability that the sum of the two rolls is 5 is 0.455.
