# Probability of AT LEAST one: 5 red, 4 green, 6 blue; pick 5 balls at random.

#### shagy

##### New member
Hi, I am working on a homework assignment from my uni and i don't understand how to calculate one question.
The question is if i have 5 red balls, 4 green balls, 6 blue balls and we get 5 balls at random.

Now i know that all the combinations for these 5 balls are 3003.
I also know that the probability for those five balls to be all blue is 6/3003.
Another thing i know is the probability of the 5 chosen balls to NOT have green balls is 462/3003.
I am guessing that for the 5 chosen balls to have 1 red, 1 green and 3 blue balls is maybe 1260/3003.

But i don't understand how to calculate the probability of AT LEAST ?
What is the probability that AT LEAST one ball is blue.

I have some examples of how to use combinations but i have no idea what to do when i am asked the question with the words AT LEAST in it and i don't have any examples in my book about this specific problem.

Can any one guide me or tell me how would they go around it ?

#### stapel

##### Super Moderator
Staff member
Hi, I am working on a homework assignment from my uni and i don't understand how to calculate one question.
The question is if i have 5 red balls, 4 green balls, 6 blue balls and we get 5 balls at random.

Now i know that all the combinations for these 5 balls are 3003.
I also know that the probability for those five balls to be all blue is 6/3003.
Another thing i know is the probability of the 5 chosen balls to NOT have green balls is 462/3003.
I am guessing that for the 5 chosen balls to have 1 red, 1 green and 3 blue balls is maybe 1260/3003.

But i don't understand how to calculate the probability of AT LEAST ?
What is the probability that AT LEAST one ball is blue.

I have some examples of how to use combinations but i have no idea what to do when i am asked the question with the words AT LEAST in it and i don't have any examples in my book about this specific problem.

Can any one guide me or tell me how would they go around it ?
Well, you should have been able to find loads of explanations and examples online, such as here. But, in short, "at least (this many)" means "not less than (this many)"; in particular, "at least one" means "not zero". What is the probability of zero? Then what is the probability of not zero?

#### shagy

##### New member
Now i know that all the combinations for these 5 balls are 3003.
I also know that the probability for those five balls to be all blue is 6/3003.
Another thing i know is the probability of the 5 chosen balls to NOT have green balls is 462/3003.
I am guessing that for the 5 chosen balls to have 1 red, 1 green and 3 blue balls is maybe 1260/3003.
Can anyone comment on these if I am making a mistake somewhere and if I am where exactly am i mistaking?

#### j-astron

##### Junior Member
shagy said:
Now i know that all the combinations for these 5 balls are 3003.
I also know that the probability for those five balls to be all blue is 6/3003.
Another thing i know is the probability of the 5 chosen balls to NOT have green balls is 462/3003.
I am guessing that for the 5 chosen balls to have 1 red, 1 green and 3 blue balls is maybe 1260/3003.

Can anyone comment on these if I am making a mistake somewhere and if I am where exactly am i mistaking?
Please show your work for all of these so that we can point out where exactly in which steps you are making mistakes. Otherwise you're just claiming an answer, and we have absolutely no idea how you got it.

stapel is giving you a super important hint. There being at least one blue ball is satisfied if there is exactly one blue ball, but it's also satisfied if there are two blue balls, or three blue balls, or four blue balls, or five blue balls. All of those cases have at least one blue ball. The only case for which it's NOT satisfied is if there are zero blue balls.