Two cards are drawn without replacement from a standard deck of 52 playing cards. what is the probability of choosing a red card for the second card drawn, if the first card, drawn without replacement, was a diamond? express your answer as a fraction or a decimal number rounded to four decimal places.

Step-by-step explanation:

Given : The total number of cards in a deck = 52

Number of red cards = 26

There are two types of red  cards : diamond and heart.

Number of diamond cards = 13

The probability that the first card is a diamond :-

Since diamond is also a red card.

Now, the total cards left = 51

The number of red cards left = 12

The probability that the second card is a red card (without repetition) is given by :-

Now, the probability of choosing a red card for the second card drawn, if the first card, drawn without replacement, was a diamond :-