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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: Southern California, USA Posts: 1,412 Thanks: 716 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: Southern California, USA Posts: 1,412 Thanks: 716 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
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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

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

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