Question

Bill Gates wrote a computer program that generates three random numbers

between 1 and 10. What is the probability that all three values will be three?

Answer 1

1/1000

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:

`p(AB)=p(A)\cdot p(B)` (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:

`s=1`

So, the probability of drawing a 3 in 1 draw is

`p(3)=(s)/(n)=(1)/(10)`

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:

`p(333)=p(3)p(3)p(3)=((1)/(10))((1)/(10))((1)/(10))=(1)/(1000)`