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Asinglecardisremovedatrandomfromadeckof52cards.Fromtheremainderwedrawtwocards at random and find that they are both spades. What is theprobability that the first ca...

Question

Asinglecardisremovedatrandomfromadeckof52cards.Fromtheremainderwedrawtwocards at random and find that they are both spades. What is theprobability that the first card removed was also a spade?

Asinglecardisremovedatrandomfromadeckof52cards.Fromtheremainderwedrawtwo cards at random and find that they are both spades. What is the probability that the first card removed was also a spade?



Answers

A card is drawn from a deck and replaced, and then a second card is drawn.
(a) What is the probability that both cards are aces?
(b) What is the probability that the first is an ace and the second is a spade?

In this question, it is told that we are going to take out three cars a little 52 cars. Okay. And in the first portion, it is told that we have to find the probability that the first to our state and then we need here. After today it's food. It is told that we need your heart means I can say that first is paid, then spared and then are okay. No, we need here. The probability of state. So we can see that the probability of speed is given by spared are 13 year, so 13 by 52 then against her. So then the Spirit turns out into 12 and the total are now 51 then heard thirties again 13 and 13 by 50 Our total cards after saloon it we can say that after simplifying it, we got here 13 divided by 8:50. So this is the answer for the first question. In the second question, it is not told that the first must be scared. It is a store that we have to find. The probability of getting any randomly who spared and one part. Now we know that out of the P two cars, we have 13 square cards, so a lot of them, we want to take two spirits, so this is given by 13 C two and we have to take out one heart out of 13 hours, that is given by 13 7, and the total number of outcomes are given by. We can see that There are 52 cards, so 50 to say three after solving it, we can say that we get here 39 by Period 50. So this is the answer for the second question here. Okay, thank you.

So we're going to cards without replacement from an ordinary deck when we want the probability. Second is black. Given First is states. To thing to note here is that spades is a black and Clovers or your blacks as well. So we've taken one of the deck. So we have 51. And we've also taken one success, which will have 26 possible successes from our first draw. And now we're left with 25. Since we've drawn one out, we'll have a 25 out of 51 verifiable.

You know this problem? We are told that two cards are drawn in succession from a deck without replacement. They want to find a probability distribution for the number of spades. Now, in a deck we have 13 spades. Yeah. And 39 non spades for a total of 52 cards. Now it's a list or sample space. Now, notice here, that means the probability of a spade is 13/52 which is 1/4. And so the probability of a non spade is 3/4. Oh, we could have a non spade followed by a non spade. It's gonna be 34 times three fours. Which means that the probability of 9/16 we could have a non spade followed by a spade. Let's get back on this first one. It is with replacement and with replacement. So it will be 3/4 for the first pick, within 38/51 for the second. A 3/4 over 434 times 38/51 for the second non spade. And so multiplying this, three divided by 51 is 17. Then we invited to out of these. Yeah, so it would be 19/34. That's the probability of two non state, 19/84. Now for a non state and then a spade. We have a 3/4 chance at the first one is a non spade and then a 13 out of 51 chance of the next one is a spade. Because we still have 13 spades left, not only 51 cards total three divided by 13 or 51 by three is 17. And so this gives us 13/68. We could have a spade and then a non spade. It's a 1/4 chance of that being spayed. And then a 39/51 chance that the next one is. Yeah. And so this will also give us 13/68 or we could have two spades. If we have two spades, there's a 1/4 chance. The first ones of spade Within a 12 51st chance of the next one is a spade. 12, divided by four is three, 3/51 is 1/17. And so here are probabilities. So for our distribution function, yeah, we could have zero spades and we found that the probability of two non spades is 19/34. So the probability okay, that at zero is 19/34. Now, we could have won and if X is one, we had a 13/68 another 13/68. So, adding those together gives us a 13/34 chance or coming up with two spades and there's no 1/17 chance of that. So here's our probability density function.

Gates. We want the probability that we draw second face. Given we Drew first was a Jack Jack. And so then we've taken one card out, and then Jack is a face card until we're gonna color Jack Queen and King's face. So we're gonna have four of each to That will leave us 12. We've taken on the jacks out, so we have 11 out of 51.


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