Here are the sample spaces of a few standard probability experiments that we have been and will be discussing:
Drawing a card at random from a standard 52-card deck
Obviously the sample space is the 52 cards in the deck; but it can be useful to have the image (from wikipedia):
Rolling a pair of six-sided die
Since there are 6 possible outcomes for the 1st die and 6 possible outcomes for the 2nd die, there are 6*6 = 36 outcomes in the sample space. It is useful to arrange these outcomes in a 6-by-6 matrix:
(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) |
Flipping a coin 2 times in a row
In this experiment, there are 4 distinct outcomes in the sample space:
S = {HH, HT, TH, TT}
If we consider the experiment of flipping a coin 3 times in a row, there are 2^3 = 8 distinct outcomes in the sample space:
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Exercise: You should try to draw these two experiments/sample spaces as tree diagrams! Also try to write out the sample space for the flipping a coin 4 times in a row. Hint: there are 2^4 = 16 distinct outcomes in that sample space.
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