Probability Question Doubt

goelmohit2002 wrote:Hi All,

Can anybody please help in solving the below probability question ? How to approach this question. As drawing 10th card in my opinion is dependent of many possibilities of reaching to 10th Card. Two examples are

SSSSSSSSSH
HHHHHHHHHH

How to count all these possibilities ?

"Laura has a deck of standard playing cards with 13 of the 52 cards designated as a "heart". If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart ? "

Answer = 1/4.

Thanks
Mohit

Yes, it would seem that P(10th card is a heart) is dependent on the 9 cards before it, but it isn't. I can illustrate this with an example.

Ann is alone in a room. She shuffles the deck, deals out 10 cards, and notes whether or not the 10th card is a heart.
She then places all 52 cards on a table and asks you to choose a card.
You choose a card, and Ann asks "What is the probability that your card is a heart?"
Well, you know that 13 of 52 cards are hearts, so the probability that this card is a heart is 13/52 or 1/4
Are you confident that this is the correct probability? You should be.
But then Ann says, "That card you just chose is the 10th card I drew from the deck."
Do you want to change your ealier answer of 1/4? What would you change it to?
Then Ann says, "Oh, maybe that isn't the 10th card; I lost track of where I put it."
So, now what is your answer? Is it 1/4? Or does your answer depend on Ann's ability to correctly tell you whether or not the card you chose is the 10th card she drew from the deck? As you can see, Ann's memory plays no part in this question. Regardless of whether it is Ann's tenth card or your first card, the probability that that card is a heart is 1/4.

I hope that helps.