Probability of Correctly Predicting 6 Numbers from 45

  • Thread starter Thread starter Sirsh
  • Start date Start date
  • Tags Tags
    Probability
AI Thread Summary
The discussion focuses on calculating the probabilities of correctly predicting six numbers drawn from a pool of 45. For exactly four correct predictions, the probability is calculated as 45C4/45C6, yielding approximately 1.83%. For at least four correct predictions, the calculation involves multiple combinations, resulting in a probability of about 7.317%. Participants express confusion over the calculations and the interpretation of "at least four," prompting clarifications on the counting methods used. The conversation highlights the complexity of combinatorial probability and the need for accurate counting techniques.
Sirsh
Messages
262
Reaction score
10
Six numbers are randomly selected from 45 numbers. Once a number is selected it is not replaced. Determine the probability of correctly predicting:

a) exactly four of the six numbers

b) at least four of the six numbers.

a) 45C4/45C6 = 1.83% chance

b) 45C4*4 / 45C6 = 7.317%
if anyone would be able to help, thanks alot.
 
Last edited:
Physics news on Phys.org
You can also approach the question like this: suppose I write down 6 numbers and ask you to perform the draw. What is the probability that you get precisely 4 of them correct, and two of them wrong?

First let me ask you if you are positive about your answer, because I got something (much) smaller. If not, can you explain how you were led to this?
 
Sirsh, your counting in the numerator of a isn't correct; in b, think about what the phrase "at least 4" means in terms of the number correct.
 
Six numbers are randomly selected from 45 numbers. Once a number is selected it is not replaced. Determine the probability of correctly predicting:

a) exactly four of the six numbers

b) at least four of the six numbers.

a) 4C4/45C6

b) 4C4+4C3+4C2+4C1+4C0 / 45C6

i'm completely puzzled..
 
OK, so suppose you have these six numbers. Then the question is: if you pick six number from a total of 45, what is the probability that exactly four of them match four of the chosen ones.

1) what is the probability that the first number picked is one of them?
2) same question for the second one, if you indeed picked one
3) now what is the probability that you first pick four of the six chosen numbers
4) what is the probability that the next two numbers are not the remaining two?
 
1) what is the probability that the first number picked is one of them?

6C1 out of 45C6?

with the other one's I am unsure, my school has supplied me with virtually no materials to learn probability with neither which i can find on the internet, sorry.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
View full post »

Similar threads

Probability of Receiving 2-4-6-7-Queen-King Sequence from 40 Cards
Replies
2
Views
1K
How to calculate the probability of winning top prize of lottery?
Replies
1
Views
1K
Probability of selecting two white balls from two bags
Replies
2
Views
3K
Chance of Selecting Twins from Group of 30 [Solved!]
Replies
24
Views
2K
Choose a ball at random from a randomly selected box - alternative way
Replies
10
Views
2K
Probability/Combinatorics: # ways of picking 5 from 3 groups of 6
Replies
7
Views
2K
Roll 5 Dice Simultaneously: Probabilities and Conditional Probability
Replies
11
Views
3K
Typo in an example (Probability)
Replies
8
Views
2K
What Is the Probability of Winning a Prize in Tattslotto?
Replies
6
Views
3K
I Total Winning Saddlecloth Numbers
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top