Question

A fair six-sided die is being rolled twice. Which of the following samples spaces is equiprobable?

S¹ ={ the second roll is less than 3 , the second roll is greater than 4 , the second roll is equal to 3 or 4}
S² ={ the second roll is odd, the second roll equal to 4 , the second roll is either a 2 or a 6
S³ ={ exactly one 6 is rolled, both rolls are 6 s, no 6 s are rolled
A. only S³ is an equiprobable sample space
B. only S² is an equiprobable sample space
c. S¹ and S³a re the only equiprobable sample spaces
D. all of them are equiprobable sample spaces
E. only S

Answer 1

The equiprobable sample spaces are S² and S³. S¹ is not equiprobable.

Step-by-step explanation:

The equiprobable sample spaces are S² and S³.

In S², the second roll is either odd, equal to 4, or a 2 or 6. These three outcomes are equally likely, so S² is equiprobable.

In S³, the possible outcomes are: exactly one 6 is rolled, both rolls are 6s, or no 6s are rolled. These three outcomes are also equally likely, so S³ is equiprobable as well.

S¹ is not equiprobable because the second roll being less than 3 has only two outcomes (1 and 2), while the second roll being greater than 4 has only one outcome (6). Therefore, the correct answer is C, only S² and S³ are equiprobable sample spaces.