Question

Which of the following are random experiments? Which are not? For those which are random experiments, describe the sample space of all possible outcomes. (a) Roll two dice and multiply together the two numbers showing. (b) Roll two dice and check if the dice are the same colour. (c) Toss a fair coin 16 times and count the number of times you got heads. In each sample space find two events which are mutually exclusive and exhaustive. Find three events which are exhaustive but not mutually exclusive.

Answer 1

A Random Experiment is an experiment, trial, or observation that can be repeated numerous times under the same conditions. The outcome of an individual random experiment must be independent and identically distributed. It must in no way be affected by any previous outcome and cannot be predicted with certainty.

(a) Roll two dice and multiply together the two numbers showing.

yes

sample space is

(b) Roll two dice and check if the dice are the same colour.

No, color will always the same.

(c) Toss a fair coin 16 times and count the number of times you got heads.

Yes,

sample space is {0,1,2,...,15,16}

two events are mutually exclusive or disjoint if they cannot both occur at the same time.

a set of events is jointly or collectively exhaustive if at least one of the events must occur

for c)

Event that number of heads is 0 and event that at least one head occurs are mutually exclusive and exhaustive

A- get less than 5 heads

B - get at least 2 heads

A and B are not mutually exclusive, but exhaustive