Conditional Probability

[Luis Felipe]

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]

probability is 1/4 .

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

[Luis Felipe]

Hmm thank you!

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

[vinux]

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]

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]

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.