Some examples of experiments and their sample spaces are as follows. (a) If the outcome of the...

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Some examples of experiments and their sample spaces are as follows. (a) If the outcome of the experiment is the gender of a child, then S = { g , b } where outcome g means that the child is a girl and b that it is a boy. (b) If the experiment consists of flipping two coins and noting whether they land heads or tails, then S = {(H, H), (H, T), (T, H), (T, T)} The outcome is (H, H) if both coins land heads, (H, T) if the first coin lands heads and the second tails, (T, H) if the first is tails and the second is heads, and (T, T) if both coins land tails. (c) If the outcome of the experiment is the order of finish in a race among 7 horses having positions 1, 2, 3, 4, 5, 6, 7, then S = {all orderings of 1, 2, 3, 4, 5, 6, 7} The outcome (4, 1, 6, 7, 5, 3, 2) means, for instance, that the number 4 horse comes in first, the number 1 horse comes in second, and so on. (d) Consider an experiment that consists of rolling two six-sided dice and noting the sides facing up. Calling one of the dice die 1 and the other die 2, we can represent the outcome of this experiment by the pair of upturned values on these dice. If we let ( i , j ) denote the outcome in which die 1 has value i and die 2 has value j , then the sample space of this experiment is S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} Oct 17 2014 12:29 PM

 

Solution ID:609266 | This paper was updated on 26-Nov-2015

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