Question

Determine the probability of the given opposite event.What is the probability of rolling a fair die and not getting an outcome less than 3?

Answer 1

The Opposite Event rule is the probability that event A happens is equal to one minus the probability that A does not happen.

If P(A) is the probability of A happening, and N(A) is the probability of A don't happen, we can write:

`P(A)=1-N(A)`

Now we can see:

`N(A)=1-P(A)`

This, we if we calculate the probability of getting less than 3, ve can calculate the probability of not getting less than 3.

Then, what are the results that are less than 3? Those are 1 and 2. Thus are the favorable outcomes, and since is a fair dice, there are 6 total possible outcomes.

The probability of A = getting less than 3, is:

`\begin{gathered} P(A)=(2)/(6) \\ P(A)=(1)/(3) \end{gathered}`

Now we can calculate the probability of not getting less than 3:

`\begin{gathered} N(A)=1-(1)/(3) \\ \end{gathered}`
`N(A)=(2)/(3)`

The probability of not getting less than 3 is:

`Probability=(2)/(3)\approx0.666`

Or in percentage:

`Probability=66.67\%`