Probability of winning if I get queen of hearts as 2nd card?

Question

I have a question from Statistics by Freedman, Pisani, and Purves:

I don't understand the way that the textbook did the problem. Why is it not (51/52)*(1/51) since 1. the card drawing is w/o replacement, 2. the first card can't be queen of hearts else its impossible for the second card to be queen of hearts. So the probability of the first card has to be 51/52

I know the textbook answer comes out to is also 1/52 but I don't understand their reasoning.

Thanks in advance for any help!

Answer 1

For part a)

Each position is equally probable for the well shuffled deck. So Queen Hearts being in second (or any) position is 1/52.

part b)

Although initially it was still 1/52, after seeing the first card the probability is now 1/51 (one in remaining 51 cards).

Answer 2

"Why is it not (51/52)*(1/51) since 1. the card drawing is w/o replacement"

If you do this calculation, you will find that your solutions is also correct (51/52)*(1/51) = (51*1)/(51*52) = (1/52). Your instinct to solve this problem is correct, the book just explains it in a different manner.