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 4,410 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: Recall probability formula

The probability of an event $A$, $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.

Step2: Identify values

The number of favorable outcomes (winning) is $1$, and the total number of outcomes is $4410$.
So, $P(A)=\frac{1}{4410}$.

Step3: Calculate $P(A)$

$P(A)=\frac{1}{4410}\approx0.00023$

Step4: Recall complement - probability formula

The probability of the complement of an event $A$, $P(\overline{A}) = 1 - P(A)$.

Step5: Calculate $P(\overline{A})$

$P(\overline{A})=1-\frac{1}{4410}=\frac{4410 - 1}{4410}=\frac{4409}{4410}\approx0.99977$

Answer:

$P(A)\approx0.00023$
$P(\overline{A})\approx0.99977$