Probabibility Independent events

[Mathematicsresear]

Homework Statement

Why is it that the probability of getting a queen in my second draw given that the first card was a spade, independent events? What if the first card drawn was the queen of spades?

Homework Equations

P(A and B)=P(A)P(B)

 

[Eclair_de_XII]

How many queens are there in a deck of cards after drawing one non-queen card?

How many cards are there in the deck after drawing your first card?

 

[Orodruin]

What if the first card drawn was the queen of spades?

What if it was another spade?

 

[PeroK]

Homework Statement

Why is it that the probability of getting a queen in my second draw given that the first card was a spade, independent events? What if the first card drawn was the queen of spades?

Homework Equations

P(A and B)=P(A)P(B)

It's clear that the first card and the second card are not independent. The probability that the second card is a spade depends on whether the first card is a spade etc.

But, does the probability that the second card is a queen depend on the suit of the first card?

You can try to resolve the issue as follows:

Before we start we know that the probability that the second card is a queen is 1/13.

Then, we draw the first card and I look at it and tell you it's a spade.

Now, is the second card more likely or less likely to be a queen? Or, is it still 1/13?

What if the first card was a diamond? Or a heart? Or a club?

Perhaps it's clear, therefore, that the denomination of the second card does not depend on the suit of the first card?

Finally, however, I would recommend checking this out using conditional probabilities. It's a good exercise in any case.