If a pair of dice is thrown twice, what are the possible outcomes?

I think it'll be 6^{4}=1296 as when two dice are are thrown simultaneously, the number of outcomes are equal to a dice thrown twice, i.e. 6^{2}=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., 6^{4}=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 6^{2 }= 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 =

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