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 3,888 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)=0.00026 (round to five decimal places as needed.) what is the value of p(\overline{a})? p(\overline{a})= (round to five decimal places as needed.)

Explanation:

Step1: Recall probability formula

The probability of an event $A$, $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Here, the number of favorable outcomes (winning) is 1 and the total number of outcomes is 3888. So $P(A)=\frac{1}{3888}\approx0.00026$.

Step2: Use complementary - probability formula

The probability of the complement of an event $A$, denoted as $P(\overline{A})$, is given by $P(\overline{A}) = 1 - P(A)$.
Since $P(A)=\frac{1}{3888}\approx0.00026$, then $P(\overline{A})=1 - 0.00026=0.99974$.

Answer:

$P(\overline{A}) = 0.99974$