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A card is randomly selected from a standard deck of playing cards. Find the probability that it is a face card, given that a black card is drawn

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Answer:

This is a very strange question because how would you know if a card drawn from a standard deck was black unless someone looked at it? And if they did look at it, they would know whether or not it was a king.

Let's assume that you have someone discretely look at the chosen card and simple tell you whether or not it was black, without disclosing the rank. This would continue until a black card was chosen. This shouldn't take too long since half of the cards in a standard deck are black, yielding a 1 and 2 change on each choosing, assuming replacement after each draw. But then, wouldn't it make more sense to simple remove all the red cards and blindly choose one of the remaining 26 black cards?

In any event, there are 4 kings in a standard deck of 52 cards. The odds would be 4 in 52 of drawing a king. Now, if you knew for sure that the card was black, the odds are equivalent to if you had blindly chosen a card from the 26 black cards.

Since there are only 2 black kings, the probability would be 2 in 26, which reduces to 1 in 13.

Step-by-step explanation:


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The probability of drawing a face card given that the card is black is:

P  = 0.23

How to find the probability?

We want to find the probability that the drawn card is a face card, given that is a black card.

There are 52 cards on a deck, 26 of these are black, we only care about these black cards.

Out of these 26 cards, 6 are face cards.

J, Q, and K of spades and J, Q, and K of clubs.

So, 6 out of 26 cards meet the condition, and we assume that all the cards have the same probability of being randomly drawn, then the probability of drawing a face card is equal to the quotient between the number of face cards and the total number of black cards.

P = 6/26 = 0.23

If you want to learn more about probability, you can read:

https://brainly.com/question/251701

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