# Exercise in Probability - balls drawn from a box

#### evinda

##### Well-known member
MHB Site Helper
Hey!!! I need some help at the following exercise...

We have a box with balls and 10% of them are red. If we choose at random 20 balls with replacement, which is the probability to pick more than 3 red balls???

#### Klaas van Aarsen

##### MHB Seeker
Staff member
Re: Exercise in Probability

Hey!!! I need some help at the following exercise...

We have a box with balls and 10% of them are red. If we choose at random 20 balls with replacement, which is the probability to pick more than 3 red balls???

Welcome to MHB, evinda!

This is about a binomial distribution.
Do you have notes on that?

Can you say for starters what the probability on exactly 0 red balls is?

#### Jameson

Staff member
Re: Exercise in Probability

Hey!!! I need some help at the following exercise...

We have a box with balls and 10% of them are red. If we choose at random 20 balls with replacement, which is the probability to pick more than 3 red balls???

Hi evinda,

Welcome to MHB! It seems to me this is the binomial distribution, but maybe it's not necessary to worry about that if you haven't been introduced to this distribution. How would you find the probability that all twenty balls are red?

I see that I like Serena has beaten me to a reply but I still want to say hello and welcome.

Jameson

#### evinda

##### Well-known member
MHB Site Helper
Re: Exercise in Probability

Welcome to MHB, evinda!

This is about a binomial distribution.
Do you have notes on that?

Can you say for starters what the probability on exactly 0 red balls is?
The probability on exactly 0 re balls is P(X=0)={20 choose 0}(0.1)^0*(0.9)^(20-0)=(0.9)^20...

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Hi evinda,

Welcome to MHB! It seems to me this is the binomial distribution, but maybe it's not necessary to worry about that if you haven't been introduced to this distribution. How would you find the probability that all twenty balls are red?

I see that I like Serena has beaten me to a reply but I still want to say hello and welcome.

Jameson
The probability that all 20 balls are red is {20 choose 20}*(0.1)^20*(0.9)^(20-20)=0.1^20...

Thank you very much!!!!!!!

#### Jameson

Staff member
Re: Exercise in Probability

So you are familiar with binomial distribution, great! That will make this much easier to do. There is one "trick" you can use here to make this calculation much easier. Let $X$ be a random variable which represents the number of red balls drawn. $$\displaystyle P[X >3]=1-P[X \le 3]$$. So instead of over 15 probabilities to calculate now you should be able to solve this through 4 calculations. Do you see how?

#### evinda

##### Well-known member
MHB Site Helper
Re: Exercise in Probability

P(X>3)=1-P(X<=3)=1-(P(X=0)+P(X=1)+P(X=2)+P(X=3)), where P(X=i)={20 choose i}(0.1)^i*(0.9)^(20-i), i=0,1,2,3...Right???

#### Klaas van Aarsen

##### MHB Seeker
Staff member
Re: Exercise in Probability

Right!

#### evinda

##### Well-known member
MHB Site Helper
Re: Exercise in Probability

Ok,thanks!!!!!