Question

Find the probability of winning a lottery if you must correctly select 4 numbers, each an integer from 0 to 9. The order is important. Assume that lottery numbers are selected at random. Express your answer as a fraction in simplest form

The probability of winning is

Answer 1

Each time you guess, you have a 1 in 10 chance of getting it correct. Doing this 4 times means you divide by ten each time you guess. This means you have a 1/10,000 chance of getting it correct.

Answer 2

Using the Fundamental Counting Theorem, it is found that the probability of winning is given by:

$\frac{1}{10000}$.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with $n_1, n_2, \cdots, n_n$ ways to be done, each thing independent of the other, the number of ways they can be done is:

$N = n_1 \times n_2 \times \cdots \times n_n$

In this problem, for each of the four digits, there are 4 outcomes, hence the total number of outcomes is given by:

$T = 10^4$.

There is only one winning combination, hence the probability of winning is given by:

$p = \frac{1}{10^4} = \frac{1}{10000}$

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866

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