A mindbender..any odds calculaltion people ou there ?

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carson

carson

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Just an attempt to get you away from current events; it's good for the Soul.

  Play Solitaire on the computer ? Sure you do. Try this for a winning streak.

  Pulled up the game and dealt. Every card was black.(no Aces) OHOH. Next select the first card to hopefully get a playable card. It was black also...and every next card was black as well.
  I gave up.
  For the Odds makers.. what are the chances of this ever happening again ? My calculator/brain isn't big enough.  :-[

  ps: I will not be liable for incidental brain damage. :D

  Florida 72 ? F



 
More seriously
For a single full pack, chance of drawing a black is 26 out of 52. =1/2
Chance of a second black is now 25/51.
So two blacks one after another is 1/2 x 25/51
3 blacks = 1/2 x 25/51 x 24/50
I leave you to actually do the math as I don't want to spoil it for you.
 
There is a huge difference between "chances" and "odds".

Buying two lottery tickets doubles your chances, but has very little effect on the odds of winning.
 
Good point, Lou.  edit: What are the odds of it ever happening again" to get a deal-out like that.

 
Sorry to simplify
1 chance in 26x25x24x23x22x21x20/52 of drawing 7 black cards
 
But that's not all.  The deal out is one thing - 7 black cards.
The other thing is the drawing of every third card from the remaining deck (45) were also black. Reds were required.

Are we into the 1 in a billion now ?
 
That's a good one, Carson.

There are 26 black cards and 26 red cards in a deck.

Seven cards are dealt as face cards, leaving 45 cards remaining in the deck.  But 21 of them are hidden behind the face cards, leaving 24 cards to draw from.

If you draw 3 at a time, you'll draw 8 times, and since 3 goes into 24 evenly, if you can't play a card during that round the game is over.

You'll have drawn a total of 15 cards, 7 face cards and 8 from the remaining deck.

So the question is, what are the odds of drawing 15 black cards in a row from the deck? (26/52)*(25/51)*(24/50) ... etc.  If I punched all of the numbers into the calculator correctly, it's 580,027 to 1.

I suspect drawing one card at a time to get 26 24 black cards in a row is a much higher number.  ;)



 
My apologies, you are right Lou, I simplified it too far, the denominator decreases by one on each draw as well as the numerator, as I wrote in the second posting.
Compared to winning a lottery those odds are pretty good, no they are excellent. I guess that's why I figure that buying a lottery ticket is an act of charity rather than a balanced financial decision.
 
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