A standard deck of has 52 cards, and contains 13 cards of each of the four suits: diamonds, spades, hearts, and clubs. What is the probability that you choose a spade, given that you have already chosen a diamond (and have not replaced it)?

so have a diamond, which means there are 51 cards left, of which 13 are still spades

Prob(spade) = 13/51

To calculate the probability of choosing a spade given that a diamond has already been chosen and not replaced, we need to determine the number of spades remaining in the deck after choosing a diamond.

Step 1: Determine the number of diamonds in the deck
Since a diamond has already been chosen and not replaced, there are now 12 diamonds remaining in the deck.

Step 2: Determine the number of spades in the deck
In a standard deck, there are 13 cards of each suit. Since we know there are 52 cards in total and there are 4 suits, there are a total of 4 * 13 = 52 spades in the deck.

Step 3: Determine the number of cards remaining in the deck
After choosing a diamond, the number of remaining cards in the deck is 52 - 1 = 51 cards.

Step 4: Determine the number of spades remaining in the deck after choosing a diamond
Since there are 52 spades in total and we have not yet chosen any spades, there are still 52 spades remaining in the deck.

Step 5: Calculate the probability of choosing a spade given that a diamond has already been chosen
The probability of choosing a spade given that a diamond has already been chosen is given by the number of spades remaining divided by the total number of remaining cards: 52 / 51.

Therefore, the probability of choosing a spade, given that you have already chosen a diamond and have not replaced it, is 52/51 or approximately 1.02.

To calculate the probability of choosing a spade, given that you have already chosen a diamond, we need to consider the number of spades remaining in the deck.

Let's break down the problem step by step:

1. To start with, the deck has 52 cards, and you have already chosen a diamond. So, we can remove the chosen diamond from the deck, which leaves us with 51 cards.

2. Now, we need to determine the number of spades remaining in the deck. Initially, there were 13 spades in the deck. However, since we have removed one card (diamond) from the deck, there are now 12 spades remaining.

3. Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the number of favorable outcomes is 12 (remaining spades) and the total number of possible outcomes is 51 (remaining cards in the deck).

Therefore, the probability of choosing a spade, given that you have already chosen a diamond, is 12/51, which simplifies to 4/17 or approximately 0.235 (rounded to three decimal places).