Question

Write down the sample spaces for the following experiments:-
(i) A coin is tossed and at the same time a die is rolled.
(ii) The order in which a mouse, a frog, and a rabbit arrive at a lake is observed.

Answer 1

Answer on Question #75763 – Math – Statistics and Probability

Question

Write down the sample spaces for the following experiments:

(i) A coin is tossed and at the same time a die is rolled.

(ii) The order in which a mouse, a frog, and a rabbit arrive at a lake is observed.

Solution

(i) There are two different outcomes of a coin: Tail(T) and Head(H), for a die there are 6: 1, 2, 3, 4, 5, 6.

A result of the experiment can be represented by 2-coordinates, the first one corresponds to the coin, and the second to the die.

So the sample space looks as follows:

$$\{(T, 1), (H, 1), (T, 2), (H, 2), (T, 3), (H, 3), (T, 4), (H, 4), (T, 5), (H, 5), (T, 6), (H, 6)\}$$

(ii) Let us denote the mouse by M, the frog by F and the rabbit by R. A result of the experiment can be represented by 3-coordinates, the first, the second, the third coordinates correspond to the first, the second, the third observed object respectively.

So the sample space is

$$\{(M, F, R), (M, F, R), (F, M, R), (F, R, M), (R, M, F), (R, F, M)\}.$$

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