Respuesta :
The sample space for the experiment of tossing a coin and a six-sided die is S = {('H', 1), ('H', 2), ('H', 3), ('H', 4), ('H', 5), ('H', 6), ('T', 1), ('T', 2), ('T', 3), ('T', 4), ('T', 5), ('T', 6)}
What is the sample space for a random experiment?
Sample space is the set of all possible outcome the considered random experiment can result to.
Thus, suppose we toss a coin, then tossing a coin is a random experiment, and the sample space is {'head', 'tail'}. We ignore other outcomes like slant coin, or standing coin by assuming that coin is very thin to stand and always falls down.
For this case, the experiment is:
Tossing a coin and a six-sided die.
Assuming coin can only result in head and tail,
and that die can only result in one of those six numbers, we get:
Results of coin toss = {H , T}
Results of tossing six sided die = {1, 2, 3, ,4 5, 6}
Since the experiment's result is paired result of both coin's toss and toss of the die, so we need to get unique pairs of both's result.
The results of the experiment would be:
('H', 1)
('H', 2)
('H', 3)
('H', 4)
('H', 5)
('H', 6)
('T', 1)
('T', 2)
('T', 3)
('T', 4)
('T', 5)
('T', 6)
The order of outcomes doesn't matter, so ('H', 6) is same as (6, 'H')
Thus, the sample space for the experiment of tossing a coin and a six-sided die is S = {('H', 1), ('H', 2), ('H', 3), ('H', 4), ('H', 5), ('H', 6), ('T', 1), ('T', 2), ('T', 3), ('T', 4), ('T', 5), ('T', 6)}
Learn more about sample space of a random experiment here:
https://brainly.com/question/16955603
