. Drawing a Card Suppose that a single card is selected from a standard 52-card deck. What is the probability that the card drawn is a club? Now suppose that a single card is drawn from a standard 52-card deck, but we are told that the card is black. What is the probability that the card drawn is a club?

Does a hint help that you are doing an "A given B scenerio" these are the ones where you have already been given some info : )

To find the probability of drawing a specific card from a standard 52-card deck, we need to know the total number of favorable outcomes (the number of cards that fit our criteria) and the total number of possible outcomes (the total number of cards in the deck).

There are 52 cards in a standard deck, and 13 of them are clubs. Therefore, the probability of drawing a club is:

Probability of drawing a club = (Number of clubs) / (Total number of cards)

Probability of drawing a club = 13 / 52

Simplifying this fraction, we get:

Probability of drawing a club = 1 / 4

So, the probability of drawing a club from a standard 52-card deck is 1/4 or 25%.

Now, let's consider the second scenario where we are told that the card drawn is black. In this case, we have additional information that can affect the probability. To solve this, we need to calculate the probability of drawing a club given that the card is black.

First, we need to find the total number of black cards in the deck. There are 26 black cards since half of the deck (26 cards) are black. Out of these 26 black cards, 13 are clubs. Therefore, the number of favorable outcomes (black club cards) is 13, and the total number of possible outcomes (black cards) is 26.

Probability of drawing a club given that the card is black = (Number of black club cards) / (Total number of black cards)

Probability of drawing a club given that the card is black = 13 / 26

Simplifying this fraction, we get:

Probability of drawing a club given that the card is black = 1 / 2

So, the probability of drawing a club when we know the card is black is 1/2 or 50%.

To find the probability that a card drawn from a standard 52-card deck is a club, we need to determine the number of favorable outcomes (club cards) and divide it by the total number of possible outcomes (52 cards).

Number of club cards: There are 13 clubs in a standard deck.

Total number of cards: There are 52 cards in a standard deck.

Therefore, the probability that the card drawn is a club is:

Probability of drawing a club = Number of club cards / Total number of cards
= 13 / 52
= 1 / 4
= 0.25
= 25%

Now, let's consider the scenario where a single card is drawn from a standard 52-card deck with the additional information that the card is black.

Number of black cards: There are 26 black cards in a standard deck (clubs + spades).

Number of club cards: There are still 13 clubs in a standard deck.

Total number of cards: There are still 52 cards in a standard deck.

Therefore, the probability that the card drawn is a club, given that it's black, can be found using the following conditional probability formula:

Probability of drawing a club given that the card is black = Probability of drawing a club and the card being black / Probability of the card being black

Probability of drawing a club and the card being black = Number of club cards / Total number of cards (as determined previously) = 13 / 52 = 1 / 4 = 0.25 = 25%

Probability of the card being black = Number of black cards / Total number of cards = 26 / 52 = 1 / 2 = 0.5 = 50%

Probability of drawing a club given that the card is black = (1/4) / (1/2) = 1/4 * 2/1 = 2/4 = 1/2 = 0.5 = 50%

Therefore, the probability that the card drawn is a club, given that it is black, is 0.5 or 50%.