1. Consider a random experiment of tossing a coin three times.
(a) Find the sample space S1if we wish to observe the exact sequences of heads and tails obtained.
(b) Find the sample space S2 if we wish to observe the number of heads in the three tosses.
2. Consider an experiment of drawing two cards at random from a bag containing four cards marked with the integers 1 through 4.
(a) Find the sample space S1 of the experiment if the first card is replaced before the second is drawn.
(b) Find the sample space S2 of the experiment if the first card is not replaced.
3. An experiment consists of rolling a die until a 6 is obtained.
(a) Find the sample space S1 if we are interested in all possibilities.
(b) Find the sample space S2 if we are interested in the number of throws needed to get a 6.