Two cards are drawn without replacement from an ordinary deck of 52 playing cards. What is the

probability that the second card is a spade if the first card was not a spade?

since all of the spades are still there, but one other card is gone, the prob that the next draw is a spade is 13/51

The first card was drawn from 52 cards, giving you a probability of 1/52 cards. One for the one that was selected (it's the only one of its kind in the deck) out of 52 possible cards = 1/52. It was not put back, but remember - it wasn't a spade so all 13 spades are still in the deck, but the deck now only contains 53 cards. Now, the probability that you can draw a spade is 13 out of 53 cards, or 13/53.

Correction - I meant 13/51 cards.

To find the probability that the second card is a spade given that the first card was not a spade, we need to first determine the number of favorable outcomes and then divide it by the number of possible outcomes.

Step 1: Determine the number of favorable outcomes
Since the first card was not a spade, there are 39 remaining spades out of the 51 cards left in the deck.

Step 2: Determine the number of possible outcomes
The first card can be any card from the 51 remaining cards, and the second card can be any of the remaining 50 cards.

Step 3: Calculate the probability
The probability of the second card being a spade, given that the first card was not a spade, is given by:
Number of favorable outcomes / Number of possible outcomes
= (Number of remaining spades) / (Number of remaining cards)

Substituting in the values, we have:
Probability = (39/51) = 0.7647 or approximately 76.47%

Therefore, the probability that the second card is a spade, given that the first card was not a spade, is approximately 0.7647 or 76.47%.