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, we need to consider the number of favorable outcomes and the total number of possible outcomes.
First, let's determine the number of favorable outcomes. Since the first card was not a spade, there are 39 cards remaining that are spades (since there are 13 spades in total and we have removed one card).
Next, let's calculate the total number of possible outcomes for the second card. Since we have already drawn one card, there are only 51 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:
Number of favorable outcomes / Total number of possible outcomes
= 39 / 51
= 0.7647 (rounded to four decimal places)
So, the probability that the second card is a spade, given that the first card was not a spade, is approximately 0.7647.
To answer your question, 13/51 is not the correct probability in this case. The number 13/51 corresponds to the probability of drawing a spade for the first card with replacement (i.e., putting the card back into the deck after drawing). Since we are drawing without replacement in this scenario, the probability is different.