Answer:
1/1000
Step-by-step explanation:
The probability of two independent events A, B (independent = events that do not depend on each other) is given by the product of the individual probabilities of A and B:
[tex]p(AB)=p(A)\cdot p(B)[/tex] (1)
In this problem, the single event is "getting a 3" when extracting a random number between 1 and 10.
The total number of possible outcomes is
n = 10
While the number of succesfull outcomes (getting a 3) is only one:
[tex]s=1[/tex]
So, the probability of drawing a 3 in 1 draw is
[tex]p(3)=\frac{s}{n}=\frac{1}{10}[/tex]
Then, we want to find the probability of getting three "3" in 3 consecutive generations. These events are independent events, so we can use rule (1) to find the total probability, and we get:
[tex]p(333)=p(3)p(3)p(3)=(\frac{1}{10})(\frac{1}{10})(\frac{1}{10})=\frac{1}{1000}[/tex]
