Question 1121970: If a die is tossed nth times, what is the sample space
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe the answer will be 6^n
when n = 1, there are 6 possible outcomes.
when n = 2 there are 6*6 possible outcomes.
when n = 3, there are 6*6*6 possible outcomes.
6*6 = 6^2
6*6*6 = 6^3
do it n times, there will be 6^n possible outcomes.
it might be easier to see with flipping a coin where there are 2 possible outcomes.
flip once and there are 2 possible outcomes.
they aqre H or T
flip twice and there are 2^2 = 4 possible outcomes.
they are HH HT TH TT
flip 3 times and there are 2^3 = 8 possible outcomes.
they are HHH HHT HTH HTT TTT TTH THT THH
extrapolate from this and you can see that if you flip 4 times, you will get 2^4 = 16 possible outcomes.
it gets harder and harder to show what they are as the number of possible outcomes gets larger.
i'll try for 16, but that's as far as i will go.
they would be:
HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT
TTTT TTTH TTHT TTHH THTT THTH THHT THHH
bottom line is, if you toss the dice n times, the sample space will contain 6^n possible outcomes.
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