Drawing Cards % Chance: If I shuffle the deck and then draw from it 7 times,...

[Arma]

Firstly I shall try to explain as best I can as I am normally awful.

If I have a deck of 60 cards numbered 1-59 with the deck containing the number 1 twice.

If I shuffle the deck and then draw from it 7 times what is the chance of having both number 1s in those first 7 cards?

If I then put those cards back into the deck, reshuffle and draw 7 new cards what is the chance of drawing both number 1s again? And then if I repeat this cycle more one.

So I guess in a sense I'm asking three questions in one.

What is the chance of drawing both 1s in a starting hand of 7 once, twice and then three times in a row. When the deck is shuffled after drawing 7 cards each time

 

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[Steven G]

So basically you have 60 cards--58 are yellow and 2 are red. You draw 7 cards and want to know what the probability that you chose the two red cards.

This is a nice problem. What have you tried so far? Where are you stuck? As a math help forum we don't solve problems for students as that would not be helpful. We prefer to give hints so that the students can get closer to solving their problem.

Please read the posting guidelines. If you follow them, then you'll get help fairly quickly.

 

[Steven G]

Here is a hint. Lay out the 58 yellow cards.
In how many places can you place the first red card? How many of those places will have the red card within the first seven positions?

Next, in how many places can you place the 2nd red card? How many of those places will have the 2nd red card within the first seven positions?

 

[Arma]

Ah sorry I should of stated. I'm not a student and the example I gave was to avoid any confusion using card names since this is what happened to me in 3 Magic the Gathering games. Where as you said Steven I ended up drawing the red cards in my first starting hand three games in a row.

I asked since my knowledge and understand of maths is I will admit more on the basic side and was merely curious about the odds of such a thing happening.

 

[blamocur]

If I then put those cards back into the deck, reshuffle and draw 7 new cards

Reshuffling the deck makes the events independent. I.e., once you figure out your probabilities for one draw it will be easy to figure out the 2 and 3 in a row probabilities.