Two Card Draw

You have the following cards to choose from:

A,2,3,4,5,6,7,8,9,10

If you draw two cards at random ( without replacement ) does the sum of there face values have a higher probability of being even or odd?

The "A" has a value of 1

@joe-shmo

10 ways to draw the first card
 5 evens
  9 ways to draw the 2nd card
   5 odds
   4 evens
 5 odds
  9 ways to draw the 2nd card
   5 evens
   4 odds

cases tally, resultant sum parity
 25 e-o, o
 20 e-e, e
 25 o-e, o
 20 o-o, e

5/9 chance of being odd
4/9 chance of being even

P.S. I feel like an RHP god, getting my text to indent like that.

@bigdoggproblem said
@joe-shmo

10 ways to draw the first card
 5 evens
  9 ways to draw the 2nd card
   5 odds
   4 evens
 5 odds
  9 ways to draw the 2nd card
   5 evens
   4 odds

cases tally, resultant sum parity
 25 e-o, o
 20 e-e, e
 25 o-e, o
 20 o-o, e

5/9 chance of being odd
4/9 chance of being even

P.S. I feel like an RHP god, getting my text to indent like that.

Correct!

There are C(10,2) = 45 ways to draw two cards

The sum is even if they have the same parity:

Both even:
C( 5,2) = 10 ways
Both odd:
C( 5,2) = 10 ways

20 ways

The sum is odd if thy have opposite parity

5*5 = 25 Ways

P( even sum ) = 20/45 = 4/9

and

P( odd sum ) = 25/45 = 5/9

P.S. The reply/quote reveals none of your magic for indenting the text! Are you willing to share this valuable information, or are we "lesser's" left to marvel at your greatness?

@joe-shmo

I found the site:
https://emptycharacter.com/

I copied the Em Space from the Unicode Empty Characters section.

This is a
 test

Good find! Thanks BDP

Σ ⟷ ∫ ⬂ ↺ ℕ  🂸

You've inspired me to look for more symbols that copy/paste from unicode. This should make some math a little more readable.

https://www.vertex42.com/ExcelTips/unicode-symbols.html