In one lottery game, contestants pick five numbers from 1 through 23 and have to match all five for the big prize (in any order)

Question

2 years ago

15

In one lottery game, contestants pick five numbers from 1 through 23 and have to match all five for the big prize (in any order)

. You'll get twice your money back if you match three out of five numbers. If you buy four tickets, what's the probability of matching three out of five numbers?
(Enter your answer as a fraction in lowest terms.)

Mathematics

1 answer:

mihalych1998 [28] · Answer 1 · 2023-09-15T12:26:39+03:00

The probability of matching three out of five numbers is 153/33649

<h3>How to determine the probability?</h3>

The numbers are given as:

1 to 23

There are five matching numbers

The probability of getting a match is:

p = 5-k/n where k = 0, 1, 2

While the complement probability is

q = (n - 2)/n

Using the above formulas, the probability of getting from 5 is:

P = 5/23 * 4/22 * 3/21 * 18/20 * 17/19

Evaluate the product

P = 153/33649

Hence, the probability of matching three out of five numbers is 153/33649