I need help understanding this question

Question

Two cards are drawn without replacement from a standard deck of playing cards. What is the probability of choosing a diamond and then, without replacement, a red card? Express your answer as a fraction or a decimal number rounded to four decimal places

Answer 1

P(diamond) = 13/52 = 1/4, with a 52 card deck and no jokers

Then there's 51 cards with 12 diamonds and 13 hearts as red cards, so it's (12+13)/53 = 25/53 chance of red on the 2nd draw.

Then multiply the two probabilities together to get: 1/4 x 25/53 = 25/212 which should be slightly less than 1/8 or slightly less than 0.1250.

Answer is 0.1180 rounded to 4 decimal places.

You know that had the card been replaced, odds of a red card would have been 1/2 on the 2nd draw, and 1/4 x 1/2 = 1/8 = 0.1250, so without replacement will be slightly less.