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February 22nd, 2012, 12:52 PM  #1 
Senior Member Joined: Jan 2010 Posts: 205 Thanks: 0  Probability of selecting things in certain order
Say there are 15 red balls and 10 green balls within a container. What is the probability that I will select 1 red ball first, and then 1 green ball, in that order? So the probability that I will select a red ball on the first try is: 15/25 That much I can tell. Then there are 24 balls left, so the chances that I now select a green ball is: 10/24 I'm told I need to multiple (15/25) * (10/24) to get the probability of selecting the red ball first, then the green ball next. What I don't understand is why am I multiplying the two, and not another operation such as adding or some other formula? Because if I select the green ball first, it's 10/25, then the chances of me selecting a red ball next is 15/24. If I multiply those, the odds are exactly the same as if I draw a red ball first and a green ball second, as if I draw the green ball first and the red ball second. Are the two odds really the same? Is there a formula I can use to calculate these types of odds? 
February 22nd, 2012, 10:52 PM  #2 
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: Probability of selecting things in certain order
Your answer is correct. As a general rule, "and" is multiplication and "or" is addition. If you pick a red ball first, you have picked one out of 15 of them. So let's say it's ball R1. If you pick R1, then you still have 10 possibilities of getting a green one. You could get ball R1 with G1, or R1 with G2, or R1 with G3, etc. There's 10 ways for that to happen just on R1. If you get R2, you could still get G1 or G2, etc. If you get R3, you could still get G1 or G2, etc. So for each R1 thru R15, you have 10 ways you can get that green ball. So there's 150 ways to get one red ball and one green ball. There's 600 ways to get 2 balls in order. Or which essentially equals 25 x 24. Hence 150/600. 
September 20th, 2017, 11:13 AM  #3 
Newbie Joined: Sep 2017 From: Romania Posts: 1 Thanks: 0 
This I have understood, but what if instead of colours we have numbers, like same colored balls but from 1 to 25. How do we calculate the probability of selecting 5 balls randomly, without putting it back, and those will be in an ascending order. Ex: 1, 3, 6, 14, 20 or, 5, 9, 15, 23, 25 

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