My Math Forum Probability with cards

 Probability and Statistics Basic Probability and Statistics Math Forum

 June 21st, 2017, 01:06 PM #1 Newbie   Joined: Dec 2016 From: Argentina Posts: 5 Thanks: 0 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
 June 21st, 2017, 02:31 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 1,931 Thanks: 999 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
 June 21st, 2017, 03:05 PM #3 Senior Member     Joined: Sep 2015 From: USA Posts: 1,931 Thanks: 999 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
June 21st, 2017, 05:36 PM   #4
Senior Member

Joined: Sep 2015
From: USA

Posts: 1,931
Thanks: 999

Quote:
 Originally Posted by romsek 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

$\dfrac{\binom{5}{3}}{\binom{10}{3}}=\dfrac {1}{12}$

 Tags cards, probability

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post johny123 Probability and Statistics 1 April 18th, 2014 06:48 AM Ataloss Advanced Statistics 1 March 22nd, 2012 08:35 PM rexden1 Advanced Statistics 2 October 2nd, 2011 12:01 AM Procon Advanced Statistics 2 January 17th, 2010 05:23 PM Dracorat Algebra 6 November 27th, 2007 12:41 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top