<s>[INST] Probability of at least once out of the three tosses Suppose a pair of fair dice is tossed 3 times. Let $X$ be the sum of the outcomes at each toss. Find the probability of getting a sum of 7 (i.e., $X=7$) at least once out of the three tosses.
My attempt:
The sample space is $6^3=216.$ There are 15 combinations that gives a sum of $7$.
$$P(X=7)=\frac{15}{216}$$
I am stuck here. If a pair of fair dice is tossed 3 times, should the sample space be 36 or 216? Am I on the right path?
 [/INST] let X = getting total of 7 then sample space S={(1,6)(6,1)(2,5)(5,2)(3,4)(4,3)}=6 times
Total number of outcomes =
{(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)
 (2,1).....................(2,6)
 (3,1).....................(3,6)
 (4,1)
 (5,1) 
 (6,1),,,,,,,,,,,,,,,,,,,,,(6,6)}=6x6=36 outcomes
P(getting total 7)=p(x)=6/36=1/6
q=5/6
getting 7 atleast once 
p(x>=1)=1-p(x<1)
=1-p(x=0)
=1- ncx p^x q^n-x  , n=3 p =1/6 q=5/6
=1- [3c0 (1/6)^0 (5/6)^3-0]
=0.42
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