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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: 1,781 Thanks: 919 
1) $\begin{align*} &P[c_1 c_2 c_3 \text{ is odd }] =\\\\ &P[c_1,c_2,c_3 \text{ are all odd}]=\\\\ &\dfrac {5} {10} \dfrac 4 9 \dfrac 3 8 = \\\\ &\dfrac{60}{720}=\\\\ &\dfrac{1}{12} \end{align*}$ 
June 21st, 2017, 03:05 PM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 1,781 Thanks: 919 
2) $\begin{align*} &P[\text{sum of 3 cards is odd}] = \\\\ &P[\text{1 odd card or 3 odd cards}] =\\\\ &\dfrac{\binom{5}{1}\binom{5}{2}+\binom{5}{3}}{ \binom{10}{3}} =\\\\ &\dfrac{50+10}{120}=\\\\ \dfrac 1 2 \end{align*}$ 
June 21st, 2017, 05:36 PM  #4  
Senior Member Joined: Sep 2015 From: USA Posts: 1,781 Thanks: 919  Quote:
$\dfrac{\binom{5}{3}}{\binom{10}{3}}=\dfrac {1}{12}$  

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