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A is the event of winning a bet of $1 on the New Jersey Pick 3 lottery. The lottery involves choosing three digits (with repetition). Only one combination of the chosen three digits will result in winning.

Theprobability of an event is defined as the chance of occurrence of that event out of all the possible outcomes.

For any arbitrary event, the probability of occurrence of E is computed as shown below:

$P\left(E\right)=\frac{\text{Number}\text{of}\text{favourable}\text{outcomes}}{\text{Total}\text{number}\text{of}\text{outcomes}}$

Let $\stackrel{¯}{E}$be the outcome of non-occurrence of E (complementary event of E). Then, the probability of non-occurrence of E is given below:

$P\left(\stackrel{¯}{E}\right)=1-P\left(E\right)$

The number of ways of winning the lottery is 1.

The total number of ways of choosing three digits is 1000.

The probability of winning the lottery$P\left(A\right)$ is obtained as follows:

$$\begin{gathered} P\left(A\right)=\frac{\text{Number}\text{of}\text{favourable}\text{outcomes}}{\text{Total}\text{number}\text{of}\text{outcomes}} \\ =\frac{1}{1000} \\ =0.001 \end{gathered}$$

Therefore, $P\left(A\right)$is equal to 0.001.

The probability of occurrence for the complement of event A is computed as follows:

$$\begin{gathered} P\left(\stackrel{¯}{A}\right)=1-P\left(A\right) \\ =1-\frac{1}{1000} \\ =\frac{999}{1000} \\ =0.999 \end{gathered}$$

Therefore, is equal to 0.999.