Want to Bet on it ?
At my party to which all you good people are invited, I take out a standard deck of 52 cards with a smile and say,
"Shuffle the deck as much as you want, then divide the deck into 3 piles in any way you desire. Now my lucky cards are King, Queen and Jack. All the rest are your lucky cards. Turn over only the top card in each of the 3 piles. If any of them is a King Queen or Jack, you give me 1$. If not, I give you 1 $. Simple?"
Do you think you want to bet on it?
What is the probability of me winning this bet?
The answer is 0.5529.
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First off how the piles are made is irrelevant. The crux of the problem is I am just taking 3 cards at random from a deck of 52 and betting that at least one of them is a K, Q, or J.
Probability of first card NOT being either KQJ = 40/52
Probability of second card NOT being either KQJ = 39/51
Probability of third card NOT being either KQJ = 38/50
Multiplying these probabilities = 0.4470588
1 - 0.44705= Probability of getting at least one of the KQJ in the 3 piles= 0.55294.
You should not bet on this game. I have the edge :)