Respuesta :
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
[tex] (5,5),\ (5,6),\ (6,5) [/tex]
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 [tex] (1,2),\ (2,1) [/tex]
A total of 6, obtainable by rolling [tex] (1,5),\ (5,1),\ (2,4),\ (4,2),\ (3,3) [/tex]
A total of 9, obtainable by rolling [tex] (3,6),\ (6,3),\ (4,5),\ (5,4) [/tex]
A total of 12, obtainable by rolling [tex] (6,6) [/tex]
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:
[tex] (1,2),\ (2,1),\ (1,5),\ (5,1),\ (2,4),\ (4,2),\ (3,3),\ (3,6),\ (6,3),\ (4,5),\ (5,4),\ (6,6) [/tex]
