- Thread starter
- #1

- Apr 13, 2013

- 3,718

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???

Thanks in advance!!!

- Thread starter evinda
- Start date

- Thread starter
- #1

- Apr 13, 2013

- 3,718

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???

Thanks in advance!!!

- Admin
- #2

- Mar 5, 2012

- 8,774

Welcome to MHB, evinda!

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???

Thanks in advance!!!

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?

- Admin
- #3

- Jan 26, 2012

- 4,040

Hi evinda,

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???

Thanks in advance!!!

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

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

Jameson

- Thread starter
- #4

- Apr 13, 2013

- 3,718

The probability on exactly 0 re balls is P(X=0)={20 choose 0}(0.1)^0*(0.9)^(20-0)=(0.9)^20...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?

- - - Updated - - -

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

Thank you very much!!!!!!!

- Admin
- #5

- Jan 26, 2012

- 4,040

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?

- Thread starter
- #6

- Apr 13, 2013

- 3,718

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???

- Admin
- #7

- Mar 5, 2012

- 8,774

Right!

- Thread starter
- #8

- Apr 13, 2013

- 3,718

Ok,thanks!!!!!