Two number cubes are rolled for two separate events: event a is the event that the sum of numbers on both cubes is less than 10. event b is the event that the sum of numbers on both cubes is a multiple of 3. list the members of the sample space for event a ∩ b.

We simply have to list the cases that satisfy events A and B.

Note that there are 36 possible outcomes, since both dice can output a number between 1 and 6.

To satisfy event A, we must roll a total of less than 10. The only combinations that don't satisfy this requests are

So, every other combination satisfies event A.

To satisfy event B, we must roll a total that is a multiple of 3. Here are the possible outcomes, and which rolls lead to them:

A total of 3, obtainable by rolling

A total of 6, obtainable by rolling

A total of 9, obtainable by rolling

A total of 12, obtainable by rolling

Note that all of these combinations satisfy event A as well, except for the last one.

So, events A and B are both satisfied by the following rolls: