Is this the correct way of solve a probability question from a deck of cards?

Question

You draw a card from a standard deck of $52$ playing cards then replace it in the deck and draw a second card. Determine the probability of drawing an eight and then heart

My work:

their are $4$ eights and $13$ hearts

So the deck is out of $52$ cards, so you multiply $4/52\times13/52= 1/52$.

The answer is $1/52$.

Is this the correct way of solve thing question?

Answer 1

You are correct! For any two independent events A and B:

$$P(\text{A and B}) = P(A)P(B)$$

Because you put the card back in between, the events have no relation to each other - which card you draw the first time has no bearing on which one you draw the second time. Thus, they are independent, and you can calculate the probability in this way.

If you would like to know more, see here.