- #1
Monstrous Math
- 10
- 1
Ha! First post! Hope you guys can help me. It's not really a homework problem, but it's close enough.
What is the probability of drawing a king, a red card, and a jack from a fair deck of 52 cards, in that order, without replacement?
If you draw a red king vs. a black king it can affect the probability of drawing a red card next. Similarly drawing a red jack vs. a non-jack from the red suit for the second card will affect the probability of drawing a jack for the third card.
So I divided it into four possible cases, and added together their probabilities:
Red King, Red Suit (non-Jack), Jack:
[itex]\frac{2}{52}[/itex]x[itex]\frac{23}{51}[/itex]x[itex]\frac{4}{50}[/itex]
Red King, Red Jack, Jack:
[itex]\frac{2}{52}[/itex]x[itex]\frac{2}{51}[/itex]x[itex]\frac{3}{50}[/itex]
Black King, Red Suit (non-Jack), Jack:
[itex]\frac{2}{52}[/itex]x[itex]\frac{24}{51}[/itex]x[itex]\frac{4}{50}[/itex]
Black King, Red Jack, Jack:
[itex]\frac{2}{52}[/itex]x[itex]\frac{2}{51}[/itex]x[itex]\frac{3}{50}[/itex]
∴ summing the probabilities yields a solution of [itex]\frac{2}{663}[/itex] I believe.
This makes sense to me, but I have a friend who is arguing with me and telling me this is wrong. I'd like some confirmation either way, and if it is wrong some help with the correct approach.
I tried using WolframAlpha to check, but it wouldn't recognize my question whenever I tried to ask. If anyone knows the correct syntax for asking WolframAlpha (or Mathematica or Matlab), I'd really appreciate it.
Thanks in advance.
Homework Statement
What is the probability of drawing a king, a red card, and a jack from a fair deck of 52 cards, in that order, without replacement?
The Attempt at a Solution
If you draw a red king vs. a black king it can affect the probability of drawing a red card next. Similarly drawing a red jack vs. a non-jack from the red suit for the second card will affect the probability of drawing a jack for the third card.
So I divided it into four possible cases, and added together their probabilities:
Red King, Red Suit (non-Jack), Jack:
[itex]\frac{2}{52}[/itex]x[itex]\frac{23}{51}[/itex]x[itex]\frac{4}{50}[/itex]
Red King, Red Jack, Jack:
[itex]\frac{2}{52}[/itex]x[itex]\frac{2}{51}[/itex]x[itex]\frac{3}{50}[/itex]
Black King, Red Suit (non-Jack), Jack:
[itex]\frac{2}{52}[/itex]x[itex]\frac{24}{51}[/itex]x[itex]\frac{4}{50}[/itex]
Black King, Red Jack, Jack:
[itex]\frac{2}{52}[/itex]x[itex]\frac{2}{51}[/itex]x[itex]\frac{3}{50}[/itex]
∴ summing the probabilities yields a solution of [itex]\frac{2}{663}[/itex] I believe.
This makes sense to me, but I have a friend who is arguing with me and telling me this is wrong. I'd like some confirmation either way, and if it is wrong some help with the correct approach.
I tried using WolframAlpha to check, but it wouldn't recognize my question whenever I tried to ask. If anyone knows the correct syntax for asking WolframAlpha (or Mathematica or Matlab), I'd really appreciate it.
Thanks in advance.