Question

let a denote the event of placing a $1 straight bet on a certain lottery and winning. suppose that, for this particular lottery, there are 2,744 different ways that you can select the four digits (with repetition allowed) in this lottery, and only one of those four - digit numbers will be the winner. what is the value of p(a)? what is the value of p(\overline{a})?
what is the value of p(a)?
p(a)=\square (round to five decimal places as needed.)

Explanation:

Step1: Recall Probability Formula

The probability of an event \( A \) is given by \( P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \). Here, the favorable outcome (winning) is 1, and the total number of possible outcomes is 2744.

Step2: Calculate \( P(A) \)

Substitute the values into the formula: \( P(A)=\frac{1}{2744} \). Calculating this, \( \frac{1}{2744}\approx0.00036 \) (rounded to five decimal places).

Answer:

\( P(A)=\boxed{0.00036} \)