a) The sample space of tossing two six-sided number cubes is the set of all possible outcomes, which consists of all pairs of numbers that can be obtained by rolling two six-sided dice. The sample space can be written as:
{ (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) }
b) To find the probability of rolling pairs of the same number, we need to count the number of outcomes in the sample space where the two dice show the same number. There are 6 such outcomes: (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6). Therefore, the probability of rolling pairs of the same number is:
P(pairs) = number of outcomes with pairs / total number of outcomes
= 6 / 36
= 1/6
c) To find the probability that at least one number will be a 3, we can count the number of outcomes where at least one of the dice shows a 3 and divide by the total number of outcomes. There are 11 outcomes where at least one die shows a 3: (1,3), (2,3), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,3), (5,3), and (6,3). Therefore, the probability that at least one number will be a 3 is:
P(at least one 3) = number of outcomes with at least one 3 / total number of outcomes
= 11 / 36
Lydia tosses two six-sided number cubes.
a) list the sample space
b) what is the probability of Lydia rolling pairs of the same number?
c) what is the probability that at least one number will be a 3
1 answer