Suppose you are tasked with rolling two fair, six-sided dice and recording the r

Question

Suppose you are tasked with rolling two fair, six-sided dice and recording the results. Suppose further that one of the dice is red, and the other is blue (so you can tell them apart). You ask four different people for a sample space, and they give you the following answers:

S1 = {11, 12, 13, ..., 64, 65, 66} where 14 denotes a 1 on the red die and a 4 on the blue die, etc.

S2 = { first die is a 6, second die is a 6 }

S3 = { 1 die shows a 6, both dice show a 6 }

S4 = { both dice are even, both dice are odd, one is even and the other is odd }

For each of the sets above, state whether or not the set is a sample space. If not, state which rule it violates, and show that it violates that rule.

Explanation / Answer

S1 is a Sample Space because Sample Space would be

= {11, 12, 13,....21, 22, 23, .....64, 65, 66}

S2 Violates the rule and it is not a Sample space, because other no also can occur like 1 on first die and 3 on second die

S3 Violates the rule and it is not a Sample space, because of Same reason

S4 is sample space, because no's can either be odd or even

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