My Math Forum  

Go Back   My Math Forum > High School Math Forum > Probability and Statistics

Probability and Statistics Basic Probability and Statistics Math Forum


Thanks Tree2Thanks
  • 1 Post By romsek
  • 1 Post By romsek
Reply
 
LinkBack Thread Tools Display Modes
June 21st, 2017, 02:06 PM   #1
Newbie
 
Joined: Dec 2016
From: Argentina

Posts: 5
Thanks: 0

Question Probability with cards

There are 10 cards numbered from 1 to 10. Take out 3 cards from them.
1) The probability that the product of the numbers of the three cards is an odd number is?
2) The probability that the sum of the numbers of the three cards is an even number is?

Thank you
Asami is offline  
 
June 21st, 2017, 03:31 PM   #2
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: Southern California, USA

Posts: 1,602
Thanks: 816

1)

$\begin{align*}
&P[c_1 c_2 c_3 \text{ is odd }] =\\\\
&P[c_1,c_2,c_3 \text{ are all odd}]=\\\\
&\dfrac {5} {10} \dfrac 4 9 \dfrac 3 8 = \\\\
&\dfrac{60}{720}=\\\\
&\dfrac{1}{12}

\end{align*}$
Thanks from Asami
romsek is online now  
June 21st, 2017, 04:05 PM   #3
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: Southern California, USA

Posts: 1,602
Thanks: 816

2)

$\begin{align*}
&P[\text{sum of 3 cards is odd}] = \\\\
&P[\text{1 odd card or 3 odd cards}] =\\\\
&\dfrac{\binom{5}{1}\binom{5}{2}+\binom{5}{3}}{ \binom{10}{3}} =\\\\
&\dfrac{50+10}{120}=\\\\
\dfrac 1 2
\end{align*}$
Thanks from Asami
romsek is online now  
June 21st, 2017, 06:36 PM   #4
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: Southern California, USA

Posts: 1,602
Thanks: 816

Quote:
Originally Posted by romsek View Post
1)

$\begin{align*}
&P[c_1 c_2 c_3 \text{ is odd }] =\\\\
&P[c_1,c_2,c_3 \text{ are all odd}]=\\\\
&\dfrac {5} {10} \dfrac 4 9 \dfrac 3 8 = \\\\
&\dfrac{60}{720}=\\\\
&\dfrac{1}{12}

\end{align*}$
to keep things consistent I should note that this is

$\dfrac{\binom{5}{3}}{\binom{10}{3}}=\dfrac {1}{12}$
romsek is online now  
Reply

  My Math Forum > High School Math Forum > Probability and Statistics

Tags
cards, probability



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Probability of cards johny123 Probability and Statistics 1 April 18th, 2014 07:48 AM
Probability with cards Ataloss Advanced Statistics 1 March 22nd, 2012 09:35 PM
probability of cards with 2 players rexden1 Advanced Statistics 2 October 2nd, 2011 01:01 AM
Cards Probability Procon Advanced Statistics 2 January 17th, 2010 06:23 PM
Cards - a probability problem Dracorat Algebra 6 November 27th, 2007 01:41 PM





Copyright © 2017 My Math Forum. All rights reserved.