Calculating Probability for Bingo Game: 4 Corners, Row, and 2 Rows

[haplo3]

Hey all,
have a problem to solve for my new game game. really appreciate if someone can help me solve this issue:

* i need to calculate the probability for a given combination


1. Total number of balls in the box = 80
2. Total number of chosen balls 45
3. for simplicity we have only 1 card 5x5 (25 numbers in total)


question
what is the probability that i will get
a. 4 corners of the card?
b. any row ?
c. any 2 rows?

if someone can give me a start i will be happy

 

[alan2]

Here's a start. I'm assuming you are holding the card and the 4 corners are known. There are C(80,45) possible combinations of 45 drawn from 80. There are C(76,41) combinations that contain your 4 corners so the probability of getting all 4 corners is C(76,41)/C(80,45). Any row is similar except that there are 5 of them, each containing 5 numbers. Give it a try.

 

[haplo3]

Here's a start. I'm assuming you are holding the card and the 4 corners are known. There are C(80,45) possible combinations of 45 drawn from 80. There are C(76,41) combinations that contain your 4 corners so the probability of getting all 4 corners is C(76,41)/C(80,45). Any row is similar except that there are 5 of them, each containing 5 numbers. Give it a try.

thank you very much. for the rows because i can get 5 different combination

(c(76,41)/c（80,45))*5

is that correct?

i assume not cause it includes the probability of getting 2 rows together or 3 rows or 4 rows, right?

 

[haplo3]

is this the correct answer for 'any row'

(c(76,41)/c(80,45))*5 - ( (c(76,41)/c（80,45))^5 + (c(76,41)/c（80,45))^4 + (c(76,41)/c（80,45))^3 + (c(76,41)/c（80,45))^2 )

so change of getting a row multiply by 5 = this will give me the chance of geting 1st OR 2nd OR 3th OR 4th OR 5th

but will also give me AND 5,4,3,2 rows together - there for i deduct those

 

[blue_raver22]

I can help you with calculating the probability for your new bingo game. To start, we need to understand the basic principles of probability. Probability is a measure of the likelihood of an event occurring. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

In your case, the total number of balls in the box is 80, and the total number of chosen balls is 45. This means that there are 80 possible outcomes and 45 favorable outcomes. Now, let's look at the different combinations you have mentioned:

a. 4 corners of the card: To calculate the probability of getting 4 corners, we need to know how many ways we can choose 4 corners out of the 45 chosen balls. This can be calculated using the combination formula nCr, where n is the total number of balls (45) and r is the number of corners (4). So, the number of ways to choose 4 corners is 45C4 = 45!/(4!(45-4)!) = 45!/(4!*41!) = 45*44*43*42/4*3*2*1 = 45*11*43 = 20790. Therefore, the probability of getting 4 corners is 20790/45 = 0.0002179 or 0.02179%.

b. Any row: To calculate the probability of getting any row, we need to consider all possible combinations of numbers in a row. Since there are 5 rows in total, we need to calculate the probability of getting at least one of those rows. This can be done by adding the probabilities of getting each row individually. So, the probability of getting any row is (1/5) + (1/5) + (1/5) + (1/5) + (1/5) = 5/5 = 1 or 100%.

c. Any 2 rows: To calculate the probability of getting any 2 rows, we need to consider all possible combinations of choosing 2 rows out of the 5 rows. This can be calculated using the combination formula nCr, where n is the total number of rows (5) and r is the number of rows we want to choose (2). So, the number of ways to choose 2 rows is 5C2 = 5!/(2!(5-2)!)