# Probabibility Independent events

• Mathematicsresear
In summary, the probability of getting a queen in my second draw given that the first card was a spade, independent events, is 1/13.f

## 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)

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?

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.