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June 21st, 2017, 01:06 PM   #1
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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?

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June 21st, 2017, 02:31 PM   #2
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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*}$
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June 21st, 2017, 03:05 PM   #3
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2)

$\begin{align*}
&P[\text{sum of 3 cards is odd}] = \\\\
&P[\text{1 odd card or 3 odd cards}] =\\\\
&\dfrac{\binom{5}{1}\binom{5}{2}+\binom{5}{3}}{ \binom{10}{3}} =\\\\
&\dfrac{50+10}{120}=\\\\
\dfrac 1 2
\end{align*}$
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June 21st, 2017, 05:36 PM   #4
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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

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