determine-whether-the-events-are-mutually-exclusive-or-inclusive-then-find-the-probability-a-card-is

Question

Determine whether the events are mutually exclusive or inclusive. Then find the probability.
A card is drawn from a standard deck of cards. What is the probability that it is a 5 or a spade?

Trinity Steen · Accepted Answer

So for number 42 it&#x27;s a probability review question from previous lesson, and we&#x27;re talking about cars. Oh, a standard deck of cards has 52 in them. And if I&#x27;m drawing a five, there are 45 in a deck of cards of 52. And then if this is an or problem, that can happen to have some overlap, because there is such a thing as a US a spade of 55 of spades. So we&#x27;re gonna have to find the probability of the five. So that&#x27;s right here. And then I need to find the probability of me getting a spade. That&#x27;s what&#x27;s going to go here. So spades, um, there&#x27;s 13 of them, so there&#x27;s a 13 out of 52 chance that I can drop a spade. But then we also want to know what about, like that overlap. And so it&#x27;s including that overlap. And so, with that being said, we can, we need to subtract that possible overlap. If that was the case, there&#x27;s one that exists with five out of 52 so we go ahead ad four plus 13 and subtract one that&#x27;s going to get us 16 out of 52 and then we divide by four to reduce. That&#x27;s gonna get us for 13th. And the question the directions was asking at identify whether or not it was inclusive or exclusive, though this one is going to be mutually inclusive because of the possibility of the overlap happening.

Eric Wendland · Answer

So in this example we&#x27;re at probability Queen drawing queen or drawing. So what&#x27;s right over there? Cards? There&#x27;s gonna be 13 cards of each different suit, so we&#x27;ll be 13. Spades, diamonds. 13. So on, So on. Um and there&#x27;s Austin four Queens Be a queen of spades Queen, parts of diamond clubs. But we have to remember, when we count that Queen of Spans, it&#x27;s also gonna be counted as a spade when we first. So, since there is a queen that is a spade, they are not mutually exclusive there. We had to be careful when counting the probability of this and to make sure that we&#x27;re not double counted. First, let&#x27;s think about the probability of drawing your queen. Remember, there are four queens to told cards. And let&#x27;s also remember probability drawing a spade is gonna be equal. Thio 13 over. D&#x27;oh! Remember, since they&#x27;re inclusive and there&#x27;s gonna be a queen of spades that&#x27;s already going to be counted in our amount of spades, we have to make sure not to so probability of queen or spade gonna be equal to probability of Quinn. Remember, this includes Queen of spades in here, plus probability of spades minus in the overlap are only overlap is gonna be the queen of spades. In this case, which gonna be equal to 16 seconds, which is gonna be equal to fourth. Any time we know that the two probabilities are inclusive, we have to remember to deal of overlap. In that case, since there is a queen that is a spade and a spade that isn&#x27;t equate. That is a queen. We know they&#x27;re not mutually exclude.

Subham Jyoti Mishra · Answer

given question we have Eric offically took us through the sample space off growing one card, a campaign sweep to do elements on the post. Part of the question we haven&#x27;t even eat where the even is that scarred is drawn from medical card, and the number off of these cars and medical card is too well. So our favorable number off evens testable on Fuzeon event, where Spirit Party strong from the deck of cards. So the number of cars is 13 Connecticut, so enough becomes 13. We also know that it is people there and oh yeah, you&#x27;re responsible. Their card is both feast as well. It disappeared there, she says. Cards, uh so in spear, their option discards. So these two events are not mutually exclusive since then. In physics, even 60. Next year&#x27;s Nordic order zero for their north. Usually so the probability off his to buy Tito Anybody in this and probably the obvious basically to and probability off and into six enough this pick or do so we have to find authority. Union F Word of overkill. Probability Off minus. Probably video you. This is a clear toe. Will people eating less? 13 32 Ministry comes vote to be to apart with cheese The event by 26 11 26 is and Bobby, we haven&#x27;t even the car. Bonus heart number off hard cars, medical verses. 13. No, he&#x27;s starting and everyone knew. Car strongest hope speared number speed guards in medical crosses. 13 again fields. You know that in medical card, Peter. 15 hearts home Contacting spirits so to and intersex into this necklace. Zero because the car drone can be either a hard or the spirit can neither be it cannot be bought Super working of being able to be there for hey, Prince year therefore mutually exclusive. Since there cannot be possibility of Rohingya, Cardiges port, heart and dispute. So it can either be hard hospital No, Find out the vetting Poverty off Brody appease and not be opponent. Office is 30 and probability off office putting their 52 improbability. Oh, and off the interest is Tzeitel. So here. Wait. If I note the probability off you Enough single. Blessed be off Manus. Peer into six. This is equal to 13 point teacher. Less. 13. A phone too. Minus Siegel. 26 of 1 52 It is one baby. So? So. The abuse. He&#x27;s living by 26 MPs. One break. Thank you

Subham Jyoti Mishra · Answer

given question. We have a takeoff 52 cards and card. Is John, uh, randomly from the take off? Because so that&#x27;s name put space age. Uh, edifice with 52 here. Ban. In the worst part of Western, we have to even begin. Uh oh. Pittis saw the was in So in a different E, The, uh, card, which is strong, is off club. So the guard is club, though in the guarantee. And even if it&#x27;s a step, the card which is drawn, is a king card. How? In the coffee to tow cars. We know that down there are 14 cars. So an off well, he is 13 year turned there. Four different kings in the wake of 52 cards. Kinga, parking off time and bingo. 11 thing off spear. So pen off this war. So we have to find out whether even even apartments exclusive or not? No. For that, we can find possibility with their both E and F cannot live together or not. Now there can be a car which is king off club. And there is one such card land, derelict cars. So enough Well, he intersex and in Passaic sent have is one which is nor the quarter Tzeitel. Therefore, uh, it is Ah mm. Mark a mutually explosively one for eventually mutually exclusive there, intersex and, uh, bandits. Or to be zero. Oh, naturally explosive. No. Uh, this person we have Walter been asked to find out the badly. No appeal probability off. Interesting union. That is probably off e border either of them occurring when a card is strong. So this is a quarter, people. Let&#x27;s be off. F minus p a p in this is enough. You he distance? No, we can find the GOP off years on and off he born You know this you have best, you know, have a bone enough s happy of intersex and will end up into six left upon an office. So this badly from so to be 13 by 52 That&#x27;s or by 52 minus one basic Tito. So this is a quartile 16 by typical his full writer p no in bar deal. The question we have to even, you know, such they&#x27;re eating obscene event where the car was a strong his case And every is an event where the car which is grown political do the girls is his beard? No, we know they&#x27;re in the capital Cars. There are what is cars and 13 spirit cards. So enough being this four here and and off f it&#x27;s talk to you and the and no, he intersex enough. Where? In the car, which is strong. It is food A an ace off speed as a little spirit. With tears off spear, it is also possible. So there is one such card. So you end up going into this meeting That is one. This is a naughty quarters Eagle. So therefore, once again, Barbie, even here in the far north, Mutual excluded for even still in mutually exclusive the early of intersex and off. Um, both day, Vince, be zero. We&#x27;re here since it is not difficult. Zero, He and I are not mutually exclusive. Therefore, he intersex center. So it is horrible. Uh, no. And does extend on not piss. Just one back of people in this part. You have also been asked to find out the little probability off union If that is you or if neither of them happening and article their car is strong in the wreck affected because so the union left can speak. I just feel minus e e six. So putting the values I get the he better be no or by 52. Thus, you will be annabelle by enough stories being better people minus he introduction. That is one day Petitto this federal themselves to be 19 minutes minutes 16. It is a good for by 13. So therefore, on this question Hello? What&#x27;s brother? Oh, answer is war by talking hand narc mutually exclusive on the second part of the best in also events and normative excluding toe over whether a deal you and NFS for about.

Joshua Eastwood · Answer

asks us again about mutually exclusive events, and the first event they give us is that you&#x27;re gonna draw card from a 52 card deck, and we want to know the card is a face card. That&#x27;s the event E in the event efforts that the card is a speed. So the question is, first of all, are those mutually exclusive? And the answer would be not mutually exclusive because there are face cards that are also speed. So whenever you can have both of them occur at the same time, and then we want the probability that you get E or F. So you have to think about Okay, there&#x27;s 52 cards in the deck, so that&#x27;s our bottom. In terms of being a face card, there are 12 of those, and in terms of speeds, there are 13 of those. However, there is some overlap. There&#x27;s four overlap, so if you take 12 plus 13 you get 26. Uh, sorry, 25 26 but you subtract before their overlap and you get 21. So you have 21 out of 52 okay, And then the second part of the question says what a vote. A situation where, if then e now is that the card is a heart, an event f is that the card is a speed. So we say OK, are those mutually exclusive? And we said, Yes, those are mutually exclusive. Okay, because you can&#x27;t be a heart and spade at the same time, and then the probability that you get E or F There are four suits total, um, two of which are hearts and speed. So there&#x27;s 26 total possibilities of the others. 13 hurts and there&#x27;s 13 spades, so that&#x27;s where I&#x27;m getting 26 from. And again it&#x27;s out of 52 because this trip to cards that you&#x27;re choosing from and if you reduce that you get 1/2. So the probability of getting its heart or a spade is 1/2 and the probability of getting a face card that&#x27;s or a speed is 21 of 52

James Macpherson · Answer

Okay, so we&#x27;re being asked if the&#x27;s Air two events are mutually exclusive. Our first woman is going to be for E. The card is a face card, and if the card is a spade, so then these air not going to be mutually exclusive because you do have face cards that are spades or spin. Is that our face cards? So we&#x27;ll consider. So since Pate face cards, we&#x27;re going to be in the spades. Our event. We&#x27;ll have spades, and then we&#x27;ll have face excluding face, excluding spades, which that&#x27;s going to be a total of 13 plus. Then we&#x27;ve got her face without space, which is going to 12 so we&#x27;ll have 25. So our probability of this happening this should be E N f. So the probability of the Union F is going to be 25 over 52 you know, for a 2nd 1 So this is party. So for our part B, we&#x27;re going to have what is the probability that we have a spade in the probability that our card is a heart? So then these are going to be mutually exclusive because you&#x27;re never going to have a heart card that&#x27;s going to be spayed. Similarly, you&#x27;ll never have a spade that&#x27;s going to be a heart. And so each one is going to be 13 out of 52 52 so you&#x27;ll have 26 out of 52 for your probability, which is the same as 1/2.

Problem

Determine whether the events are mutually exclusi…

Problem 42 Hard Difficulty

Determine whether the events are mutually exclusive or inclusive. Then find the probability.
A card is drawn from a standard deck of cards. What is the probability that it is a 5 or a spade?

Answer

$\frac{4}{13}$ inclusive

Related Courses

Algebra

Related Topics

Discussion

Top Algebra Educators

Anna Marie V.

Kayleah T.

Maria G.

Kristen K.

Algebra Courses

Absolute Value - Example 1

Absolute Value - Example 2

Recommended Videos

Watch More Solved Questions in Chapter 12

Video Transcript

Holliday, Luchin, Cuevas, Carter Marks, Day, Casey, Hayek

Algebra

Anna Marie V.

Kayleah T.

Maria G.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$\frac{4}{13}$ inclusive

Algebra

Anna Marie V.

Kayleah T.

Maria G.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

Holliday, Luchin, Cuevas, Carter Marks, Day, Casey, HayekAlgebra

Anna Marie V.

Kayleah T.

Maria G.

Kristen K.

Holliday, Luchin, Cuevas, Carter Marks, Day, Casey, Hayek

Algebra