Question

in a certain lottery, you must correctly select 5 numbers (in any order) out of 25 to win. you purchase one lottery ticket. what is the probability that you will win?

the probability of winning is .
(use scientific notation. use the multiplication symbol in the math palette as needed. round to the nearest hundredth as needed.)

Explanation:

Calculate total possible outcomes

Using the Combinatorics knowledge point

$$ N = \binom{25}{5} = \frac{25 \times 24 \times 23 \times 22 \times 21}{5 \times 4 \times 3 \times 2 \times 1} = 53,130 $$

Calculate probability of winning

Using the Classical Probability knowledge point

$$ P = \frac{1}{53,130} \approx 1.8821758 \times 10^{-5} $$

Format in scientific notation

Using the Classical Probability knowledge point

$$ P \approx 1.88 \times 10^{-5} $$

Answer:

In a certain lottery, you must correctly select 5 numbers (in any order) out of 25 to win. You purchase one lottery ticket. What is the probability that you will win?

The probability of winning is <blank>\(1.88 \times 10^{-5}\)</blank>.
(Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to the nearest hundredth as needed.)