View Full Version : Conditional Probability

Luis Felipe

07-11-2010, 10:31 AM

What is the chance that the seventh card from the top of the deck will be a heart?

This question really stumped me. I thought [52_C_6 multiply 13_C_1] and then divided by 52_C_7 would be correct but the probability is greater than 1 which is obviously wrong.

Thank you!

vinux

07-11-2010, 10:48 AM

probability is 1/4 .

( since there is no information about first 6 cards).

Luis Felipe

07-11-2010, 10:59 AM

Hmm thank you!

So we don't need to multiply anything to ensure it's in the 7th place?

vinux

07-11-2010, 11:14 AM

Yes. Also you can argue that by symmetry ( chance of 7th card is heart or club or diamond or spade is same => prob is 1/4)

SadieKhan

07-11-2010, 02:20 PM

Hi,

Can you please explain it to me?I am trying to practice probability, and I do not understand how did you get 1/4?

I know 13/52 is 1/4 but don't we have to be specifically telling the probability of a card which is in 7th position?

1/4 just gives us the probability of drawing or having a heart.

Dason

07-11-2010, 02:49 PM

Hi,

Can you please explain it to me?I am trying to practice probability, and I do not understand how did you get 1/4?

I know 13/52 is 1/4 but don't we have to be specifically telling the probability of a card which is in 7th position?

1/4 just gives us the probability of drawing or having a heart.

What is the probability of the first card being a heart? Now, we know nothing about this card or the six cards following it. Now take the first card and move it to the seventh position. Should the probability that it's a heart change? No.

The reason is because we know nothing else about the other cards.

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