Associated Topics || Dr. Math Home || Search Dr. Math

### Combined Probability of Unrelated Events

```
Date: 7/23/96 at 0:25:42
From: Anonymous
Subject: Combined Probability of Unrelated Events - 5 Cards

Five cards are drawn without replacement from a standard deck of
playing cards. Next, five cards are drawn without replacement from a
second standard deck of playing cards. And finally, five cards are
drawn without replacement from a third standard deck of playing cards.

What is the probability that the Ace of Spades will appear once?
What is the probability that the Ace of Spades will appear twice?
What is the probability that the Ace of Spades will appear three
times?

Is this another Hypergeometric Distribution problem?

I know NCx = N! / (x! * (N-x)!) = 52! / (5! * (52-5)!)  =  2,598,960

But where do I go from here?  This is somewhat confusing.

Thanks
```

```
Date: 7/23/96 at 16:10:20
From: Doctor Anthony
Subject: Re: Combined Probability of Unrelated Events - 5 Cards

The chance that the Ace of Spades is chosen when five cards are dawn
from one pack is

(1C1*51C4)/(52C5) = 0.09615

Chance that it is not selected is 1 - 0.09615 = 0.903846

So we have three trials, in each of which there is a probability of
success of 0.09615, and a chance of failure of 0.903846  This is a
binomial probability problem, and we have :

Probability of one success = 3C1*0.09615*0.903846^2 = 0.235646

Probability of two successes = 3C2*0.09615^2*0.903846 = 0.0250677

Probability of three successes = 3C3*0.09615^3 = 0.0008889

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
College Probability

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search