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 1,512 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) = (round to five decimal places as needed.)

Explanation:

Step1: Calculate \(P(A)\)

The probability formula is \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (winning number) is \(1\), and the total number of outcomes is \(1512\). So, \(P(A)=\frac{1}{1512}\).

$$ \frac{1}{1512}\approx0.00066 $$

Step2: Calculate \(P(\overline{A})\)

Using the formula \(P(\overline{A}) = 1 - P(A)\). Substitute \(P(A)=\frac{1}{1512}\) into the formula.

$$ P(\overline{A})=1-\frac{1}{1512}=\frac{1512 - 1}{1512}=\frac{1511}{1512}\approx0.99934 $$

Answer:

\(P(A)\approx0.00066\), \(P(\overline{A})\approx0.99934\)