Probability using cards

sp2

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I am really struggling.. I feel like I know the answer but also that maybe I'm wrong.

THe question: A single card is drawn at random from a standard deck of 52 cards. Find theprobability of drawing the following cards.

Find the probability of a red card and a black card.

I feel like the answer is 0 b/c if you are only picking one card then it can't be both red and black? Am I missing something?
 
Personally, I think the question is a bit poorly written and ambiguous. If we interpret it to mean "Find the probability that a card drawn at random will be both red and black," then you're correct that the answer is 0 because this is impossible. However, I think it's more likely that the problem is meant to have two separate parts: "Find the probability of [drawing] a red card and [find the probability of drawing] a black card." Of course, this still leaves the question of why this is two distinct exercises - they're both going to have the same answer. But if you really want to know for sure what's going on, it's best to just directly ask the person who wrote the problem, or ask your instructor. Surely they can provide better clarification than my random guesses.
 
I am really struggling.. I feel like I know the answer but also that maybe I'm wrong.

THe question: A single card is drawn at random from a standard deck of 52 cards. Find theprobability of drawing the following cards.

Find the probability of a red card and a black card.

I feel like the answer is 0 b/c if you are only picking one card then it can't be both red and black? Am I missing something?

I agree with ksdhart2, except that I think your interpretation is what was intended. I've seen enough books give exercises with this sort of wording, where the context (surrounding exercises) makes it clear what is meant. For example, the next question might be something like, "Find the probability of a red card or a Queen". Clearly this is about a single card, and they are testing your understanding of "and" and "or", so your thinking is exactly what they want you to do.

I would prefer that they worded the exercise something like this: "Find the probability that the card drawn is both a red card and a black card". Or, it might be, "If A is the event that the card drawn is a red card, and B is the event that the card drawn is a black card, find the probability of the event A and B."

At any rate, yes, problems like this are sometimes as obvious as you think! They just want to make you think the way you did, to get you used to the idea of "and".
 
I agree with ksdhart and Dr. Peterson that if the question is indeed "a single card is drawn .... Find the probability of drawing the following cards," the question is badly written because it is impossible to get cards by picking one card. It would have been much better to write "Find the probability of the following events." (Of course, that may be what the book actually did say.)

But whatever is the text's exact wording, your rendition of the text does imply that the "red and black" card is part of a list, in which case your answer of zero is absolutely correct. Although it is possible to imagine a card that is partly red and partly black, there is no such card in a standard deck of cards. Therefore, drawing such a card from such a deck is impossible By definition, an impossible event has a probability of zero. A certain event has a probability of one. A probability of an uncertain but possible event has a probability greater than zero and less than one, with higher values indicating greater likelihood. That is the basic meaning of a numerical probability. You seem to have that basic idea. Good job.
 
I am really struggling.. I feel like I know the answer but also that maybe I'm wrong.

THe question: A single card is drawn at random from a standard deck of 52 cards. Find theprobability of drawing the following cards.

Find the probability of a red card and a black card.

I feel like the answer is 0 b/c if you are only picking one card then it can't be both red and black? Am I missing something?
To answer your question we will need to know whether or not there was another part to this question. The reason is the question asked for the probability of drawing the following cards. If there is a part b to this problem, then I feel that they are asking you for the probability of drawing a card that is both red and black. If no part b, then I guess it is two separate problems and is worded poorly.

Personally I never get troubled over these problems. If the wording can be taken to have different meanings then I just make sure that I can solve the problems with each interpretation. If it is during an in-class exam I think that it is fair to ask the instructor to clarify the problem.
 
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