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1. Describe the sample space and all 16 events for a trial in which two coins are thrown
and each shows either a head or a tail.
2. A fair coin is tossed, and a fair die is thrown. Write down sample spaces for
(a) the toss of the coin;
(b) the throw of the die;
(c) the combination of these experiments.
3. A bag contains fifteen balls distinguishable only by their colours; ten are blue and five
are red. I reach into the bag with both hands and pull out two balls (one with each hand)
and record their colours.
(a) What is the random phenomenon?
(b) What is the sample space?
(c) Express the event that the ball in my left hand is red as a subset of the sample space.
4. I have in my pocket ten coins. Nine of them are ordinary coins with equal chances of
coming up head and tail when tossed and the tenth has two heads.
(a) If I take one of the coins at random from my pocket, what is the probability that it is
the coin with two heads?
(b) If I toss the coin and it comes up heads, what is the probability that it is the coin with
two heads?
(c) If I toss the coin one further time and it comes up tails, what is the probability that it
is one of the nine ordinary coins?
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