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 given that the first card was not a spade, you can use the concept of conditional probability.
First, let's calculate the number of spades in the deck. In a standard deck of 52 cards, there are 13 spades.
Now, after the first card is drawn and it is not a spade, there are 51 cards remaining in the deck. Out of these, there are still 13 spades. So the number of favorable outcomes (drawing a spade as the second card) is 13.
The total number of possible outcomes for the second card is 51 because there are 51 cards remaining in the deck.
Therefore, the probability of drawing a spade as the second card, given that the first card was not a spade, is 13/51.
This fraction cannot be further reduced, as 13 and 51 do not have any common factors other than 1.
So, your answer of 13/51 is correct, and it does not need to be reduced any further.