If a pair of dice is thrown twice, what are the possible outcomes?
I think it'll be 64=1296 as when two dice are are thrown simultaneously, the number of outcomes are equal to a dice thrown twice, i.e. 62=36.
Hence if we throw a pair of dice two times, the outcomes would be equal to throwing 4 dice simultaneously or throwing a dice 4 times, i.e., 64=1296.
Am I correct? If not plz explain........
Then there are ques....
If a pair of dice is thrown twice, what is the probability of getting
(i) 2 as the sum of numbers (I think 1/1296)
(ii) a doublet (I think 1/36)
(iii) 8 as the sum of numbers
Someone explain please........
When two dice are are thrown simultaneously, the number of outcomes are equal to 62 = 36.
When a pair of dice is thrown twice, we get the following outcomes,
{(1, 1), (1, 2), ..., (1, 6)
(2, 1), (2, 2)..., (2, 6)
(3, 1), (3, 2), ... , (3, 6)
(4, 1), (4, 2),..., (4, 6)
(5, 1), (5, 2), ... , (5, 6)
(6, 1), (6, 2), ..., (6, 6)} = 36 on first throw
Similarly on the second throw, we get the same outcomes = 36 which means the outcomes repeat.
The total number of outcomes = 36 + 36 = 72.
Hence, these events are different.
When we throw 4 dice simultaneously,
the total outcomes are 
.
Now here is the solution for the question,
When a pair of dice is thrown twice, the total number of outcomes = 72 (as explained above)
(i) 2 as the sum of numbers
The favorable outcomes = (1, 1), (1, 1) = 2
Probability = 
(ii) a doublet
The favorable outcomes = (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) = 12
Probability = 
(iii) 8 as the sum of numbers
The favorable outcomes = (2, 6), (3, 5), (4, 4), (5, 3), (6, 2), (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) = 10
Probability = 