a number cube has faces numbered 1 to 6. what is true about rolling the number cube one time? select three…

a number cube has faces numbered 1 to 6. what is true about rolling the number cube one time? select three options. \n□s = {1, 2, 3, 4, 5, 6}\n□if a is a subset of s, a could be {0, 1, 2}.\n□if a is a subset of s, a could be {5, 6}.\n□if a subset a represents the complement of rolling a 5, then a = {1, 2, 3, 4, 6}.\n□if a subset a represents the complement of rolling an even number, then a = {1, 3}.

a number cube has faces numbered 1 to 6. what is true about rolling the number cube one time? select three options. \n□s = {1, 2, 3, 4, 5, 6}\n□if a is a subset of s, a could be {0, 1, 2}.\n□if a is a subset of s, a could be {5, 6}.\n□if a subset a represents the complement of rolling a 5, then a = {1, 2, 3, 4, 6}.\n□if a subset a represents the complement of rolling an even number, then a = {1, 3}.

Answer

Answer:

  1. S = {1, 2, 3, 4, 5, 6}
  2. If A is a subset of S, A could be {5, 6}.
  3. If a subset A represents the complement of rolling a 5, then A = {1, 2, 3, 4, 6}.

Explanation:

Step1: Define sample - space

The sample - space S of rolling a number cube numbered 1 to 6 is all possible outcomes, so S = {1, 2, 3, 4, 5, 6}.

Step2: Check subset condition

Since S = {1, 2, 3, 4, 5, 6}, a subset A of S can only contain elements from S. {0, 1, 2} has 0 which is not in S, while {5, 6} is a valid subset of S.

Step3: Find complement

The complement of an event is all outcomes in the sample - space that are not in the event. The complement of rolling a 5 in the sample - space S = {1, 2, 3, 4, 5, 6} is {1, 2, 3, 4, 6}. The complement of rolling an even number (2, 4, 6) in S should be {1, 3, 5}, not {1, 3}.