# Calculate probability of an event occuring X times

#### Maxjprg

##### New member
Hello,

my problem is as follow :

- I have 110 different bags with red and blue coins in it
- I randomly draw 1 coin from each bag
- The probability to draw a red coin from each bag is the same, I have 12.2% chance to draw a red coin from each bag
- I need 12 red coins

What is the probability that after I draw 1 coin from each of the 110 bags I have at least 12 red coins (or more) ?

Thank you very much by advance for your help

#### Subhotosh Khan

##### Super Moderator
Staff member
Hello,

my problem is as follow :

- I have 110 different bags with red and blue coins in it
- I randomly draw 1 coin from each bag
- The probability to draw a red coin from each bag is the same, I have 12.2% chance to draw a red coin from each bag
- I need 12 red coins

What is the probability that after I draw 1 coin from each of the 110 bags I have at least 12 red coins (or more) ?

Thank you very much by advance for your help
What are your thoughts/works regarding this assignment.

#### Dr.Peterson

##### Elite Member
Hello,

my problem is as follow :

- I have 110 different bags with red and blue coins in it
- I randomly draw 1 coin from each bag
- The probability to draw a red coin from each bag is the same, I have 12.2% chance to draw a red coin from each bag
- I need 12 red coins

What is the probability that after I draw 1 coin from each of the 110 bags I have at least 12 red coins (or more) ?

Thank you very much by advance for your help
It's important for you to tell us what you know about the subject, and where you have trouble on this problem. Please read this, which you should have done before submitting.

For example, do you know about the binomial distribution? How about the normal approximation to it?

#### Maxjprg

##### New member
It's important for you to tell us what you know about the subject, and where you have trouble on this problem. Please read this, which you should have done before submitting.

For example, do you know about the binomial distribution? How about the normal approximation to it?
Hello,

It's not from a class or work or anything it's to figure out a strategy for an online fantasy card game.

I would know how to calculate for example the probabiliy to get at least one red coin out of the bags which should look something like :
100-(((100-12.2)/100)^110) if i'm not mistaking (99.9999993913%)
If i'm not mistaken (12.2/100)^12 gives me the probability that I get my 12 red coins out of the 12 first bags, which is very unlikely

It's the fact that you need to draw multiple red coins among a lot of bags to be happy that confuses me, how do you factor that in

You have only 12.2% chance to get a red coin from a bag, but you do a lot of pulls (110) which increase your chance to be happy, but you want to get lucky 12 times which is a lot to ask and decreases your chances to be happy
I can't figure out how to conterbalance the increase versus the decrease basicly

From the sheer looks of it when playing it seems like the odd are around 50%, I have the impression that I pull it off around half the time but it's a very little number of tries so highly unreliable.

I don't know what are "binomial distribution" and "normal approximation" are

thanks by advance for your help

#### Maxjprg

##### New member
Hello,

I posted a message yetserday with more details but it still does not appears.
Is it still in some kind of validation process ?

thanks