Question

Flip a coin 3 times, what is 1. outcome 2. sample space 3. event(two tails) 4. event space(two tails)

Answer 1

An Experiment is any activity with an observable result. Tossing a coin, rolling a die or choosing a card are all considered experiments.

An Outcome (or Sample point) is the result of the experiment.

The set of all the possible outcomes is called the sample space of the experiment and is usually denoted by S.

Any subset E of the sample space S is called an event.

We have to flip a coin three times.

A coin has two faces i.e., Head (H) and tail (T)

1)

Each coin toss has two possible outcomes: Heads (H) and Tails (T). For k tosses, there are 2 ^k outcomes. Therefore, there are 2 ³= 8 possible outcomes when a coin is tossed three times. We can list the 8 outcomes as follows:

HHH

HHT

HTH

HTT

THH

THT

TTH

TTT

2)

Sample space = set of all possible outcome when flipping a coin three times

The sample space for flipping a coin 3 times

3)

Given

X : event of getting two tails.

Possible outcomes for getting two tails when flipping a coin three times are

4)

Event space (two tails) = Set of all possible outcome of getting two tails when flipping a coin three times.

Therefore,

Event space of getting two tails when flipping a coin three times =