Write down the sample space for rolling a pair of dice. Also write down the set of outcomes for the events (i) rolling a double (ii) getting a sum of 7 (iii) getting a sum of 1.
Write down the sample space for rolling a pair of dice. Also write down the set of outcomes for the events (i) rolling a double (ii) getting a sum of 7 (iii) getting a sum of 1.
Sample space =
{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}.
Set of outcomes for the event “rolling a double” =
{(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}.
Set of outcomes for the event “getting a sum of 7” =
{(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}.
It is not possible to get a sum of 1 when rolling two dice. Thus, the set of outcomes is the null set φ.
Sample space =
{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}.
Set of outcomes for the event “rolling a double” =
{(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}.
Set of outcomes for the event “getting a sum of 7” =
{(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}.
It is not possible to get a sum of 1 when rolling two dice. Thus, the set of outcomes is the null set φ.
