Question 1068630: When two dice are rolled, the sample space consists of how many events?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the sample space consists of all possible outcomes of the experiment.
i believe there will be 6 * 6 = 36 possible outcomes.
that's because, for every number from 1 to 6 on the first die, there are 6 possible numbers on the second die.
6 * 6 = 36 possibilities.
they are:
first die is 1, second die is 1 to 6.
first die is 2, second die is 1 to 6.
etc.
the possible numbers are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
the probabilities of getting each are different.
that's because each number is a combination of several outcomes of the roll.
probability of getting a 2 is 1 our of 36 because:
1 + 1 = 2
probability of getting a 3 is 2 out of 36 because:
1 + 2 = 3
2 + 1 = 3
probability of getting a 4 is 3 out of 36 because:
1 + 3 = 4
3 + 1 = 4
2 + 2 = 4
probability of getting a 5 is 4 out of 36 because:
1 + 4 = 5
4 + 1 = 5
2 + 3 = 5
3 + 2 = 5
probability of getting a 6 is 5 out of 36 because:
1 + 5 = 6
5 + 1 = 6
2 + 4 = 6
4 + 2 = 6
3 + 3 = 6
probability of getting a 7 is 6 out of 36 because:
1 + 6 = 7
6 + 1 = 7
2 + 5 = 7
5 + 2 = 7
3 + 4 = 7
4 + 3 = 7
probability of getting an 8 is 5 out of 36 because:
2 + 6 = 8
6 + 2 = 8
3 + 5 = 8
5 + 3 = 8
4 + 4 = 8
probability of getting a 9 is 4 out of 36 because:
3 + 6 = 9
6 + 3 = 9
4 + 5 = 9
5 + 4 = 9
probability of getting a 10 is 3 out of 36 because:
4 + 6 = 10
6 + 4 = 10
5 + 5 = 10
probability of getting an 11 is 2 out of 36 because:
5 + 6 = 11
6 + 5 = 11
probability of getting a 12 is 1 out of 36 because:
6 + 6 = 12
that's the total number of possibilities.
add up all the probabilities and you get 36/36 = 1, as you should.
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