Question

If you roll a single die and count the number of dots on top, what is the sample space of all possible outcomes? Are the outcomes equally likely?

Answer 1

Outcomes: S = {1, 2, 3, 4, 5, or 6}

The outcomes of rolling a single die are equally likely.

Explanation:

A single fair die has six faces. Each face has dots on it, numbered {1, 2, 3, 4, 5, or 6}.

On rolling the die the possible outcomes are:

S = {1, 2, 3, 4, 5, or 6}

Thus, there are a total of 6 possible outcomes.

Equally likely events are events that has the same probability of happening.

For example, if events A and B are equally likely then P (A) = P (B).

The outcomes of rolling a die are equally likely because the probability of any of the 6 faces showing up are same, i.e.

`P(1) = P(2)=P(3)=P(4)=P(5)=P(6)=(Favorable\ outcome)/(Total\ no.\ of\ outcomes)=(1)/(6)`

Thus, the outcomes of rolling a single die are equally likely.