Two cards are drawn without replacement from an ordinary deck of 52 cards. What is the probability that the second card is a spade if the first card was not a spade ?

13/51 is that correct, do I need to reduce this number?

To find the probability that the second card is a spade if the first card was not a spade, we need to consider the number of spades remaining in the deck after the first card is drawn.

First, we need to determine the number of non-spade cards in the deck. Since there are 52 cards in a deck and 13 of them are spades, there are 52 - 13 = 39 non-spade cards.

After the first card is drawn, there are now 51 cards remaining in the deck, with 39 of them being non-spade cards and 13 being spades.

The probability that the second card is a spade can be calculated as the number of favorable outcomes (drawing a spade) divided by the number of possible outcomes (drawing any card).

The number of favorable outcomes is 13 (the number of spades remaining in the deck) and the number of possible outcomes is 51 (the total number of cards remaining in the deck).

Therefore, the probability that the second card is a spade, given that the first card was not a spade, is 13/51. You do not need to reduce this fraction further as it is already in its simplest form.