for-the-experiments-in-exercises-1318-write-out-the-sample-space-s-choosing-an-s-with-equally-like-5

Question

For the experiments in Exercises 13–18, write out the sample space S, choosing an S with equally likely outcomes, if possible. Then give the value of n(S) and tell whether the outcomes in S are equally likely. Finally, write the indicated events in set notation.

A coin is flipped until two heads appear, up to a maximum of four flips. (If three tails are flipped, the coin is still tossed a fourth time to complete the experiment).
a. The coin is tossed four times.
b. Exactly two heads are tossed.
c. No heads are tossed.

Amy Jiang · Accepted Answer

Okay, so we have slips. Number 2125 and two are drawn time scandalously so we can have a one and a two. I want one. Want to? We can&#x27;t have a one and one because we draw two at once. So and there&#x27;s only one simple fun. So we have one comment to one common three. One come before or one comma. Five. We can also have a to common one, not a two comma two. So that&#x27;s to come with three to calm before and to come of five. Or we can have a three common one, three, comma two and we can&#x27;t have a degree Common three. So basically, we can&#x27;t have two numbers that are the same numbers for one for two, 43 count at 44 So 45 And lastly, we could have 51 52 five, three and 54 So this is our sample space. And for our first part report, they were asked to find, um when both ships are marked with even numbers. Okay, so I first wrote it didn&#x27;t have even numbers. Our second roll. There&#x27;s a two and a four. So that&#x27;s an even number. We can also have see a four in it, too. But that&#x27;s the same as two and four since where&#x27;s Ah, swapping them around? So what&#x27;s to say A is two comma four? Okay, Now for Part B, we have one. Slip is marked with the odd number, and the other is marked with an even number. Okay, so before I do that, let&#x27;s remove the ones that have be Pete&#x27;s. So it has to come before is the same as for comment, too. So we say one comma two is the same as two Company 31 Common three is the same as to become a one one come before is the same as for common. 115 is there was 5123 of the same is 32 25 or to foreign famous for 2 to 5 of the same. It&#x27;s far too okay, and then we have 34 that status for three 35 That&#x27;s the same as 53 and 45 is the same. It&#x27;s five years to notice that we only have our upper, um, diagonal portion. Okay, so for part B, we wanted one step is marked with an odd and the other is more cute than even. So we see 12 That&#x27;s odd. And even 13 is both hard won. Four is odd, and even when five is both odds, two and three is on and even two and four, that&#x27;s both even two and five. That&#x27;s odd and even, or even a nod. Something on 34 that&#x27;s even in off and 35. That&#x27;s both odd. 45 That&#x27;s ought. And even so, we have 123456 We have one common to one come before to common. Three to come a five three com before and lastly, we have four come with five. Okay, And now for part C, we want both slips are marked with the same number. Well, actually, this is impossible, right? Cause we&#x27;re drawn to simultaneously so we can&#x27;t have 11 because we only have one slip with one. So that&#x27;s just the empty set

Amy Jiang · Answer

Okay, So never said we have five executives will label that as well. We&#x27;ll leave with them by their first letter in each of their names. So that&#x27;s a B, C, D and E. I know we want to choose from these five people. Um, a committee of two people. So our sample space that is possible is a B or a C or a d a E, or we gonna have be see BG. Thank you. And now we can have see the noticed that I don&#x27;t do see A or C p because that&#x27;s already covered in a C on BC. So we have CD and see you. And lastly, we here we could have d e. And our e is already covered in each of these cases. Okay, so this is our sample space. So for party, we want, um, Chin is in the community. So everything was a c in it. That is, we have one to 34 So China is in a committee, um, and were asked to write that in sanitation. So that&#x27;s see or actually a C BC so you be and C e. And now for part B, we want, um Dickinson&#x27;s and I was worth are not in a community committee. So we want the, um, sample space such that we don&#x27;t have see on or d any. Okay, so we see. Um, a de here, Andy here would be here on me here. Do you hear that? You hear energy And you here. So the only possible ones are a B. They see andi, BC, and lastly for part C, we want where both Alan on chin are in a committee. So that&#x27;s just a and C together, and there&#x27;s no possible other case.

Ankit Gupta · Answer

we haven&#x27;t experiment off tossing a coin and then rolling their day so in apart. If we need to find our sample space Neymar sample spaces as so. Firstly, if we toss a coin, we can either get head or tail. And if we Lola die outcomes must be 1234 and 56 So these must be outcomes of the role or die. So the total elements in assemble space are getting ahead on one held and to help entry head and food heading 506 and for tail with the are getting pale and one male and two Palin going and the owner day pale and four they&#x27;ll and five and tail in six years that is representing head and he&#x27;s representing pill. Now in our part B, we need to find the probability off getting ah head on an even number. So name this event as e. So getting ahead on even number. We have these outcomes with that that&#x27;s too at four and at six. No number off elements in this even E is three on the total number of elements in sample space. Our bill therefore, probability that even probability that even he occur is three bite will That is number of elements and even e over a number of elements in total sample space. So we are probabilities one by food Now in part C. We need to find the probability very we have one head with a number greater than for. So consider this event as f We should have head with a number greater than four, which is number can be five or six. So we have only two outcomes. Mitt dizzle, you know, head on a number greater than four. Therefore, number of elements and even f r two and the number of elements in sample space are well, therefore, rabbit deals even after marketing is number of elements and f over number of elements in s so the daughter love to bite Well, so we have reliability won by six that even f occurs now in part B. We need to find the outcomes where we have our tail and an order number so named this even as G so in, even Devi should have our tail andan or number. So we have Stephen Petri on t five for this. So the one Petri anti five now we can see that number of elements in even G R three on number of elements in total sample space. Hartwell. So I probably that even G occurs is three bites. Well, that is number of elements in G, divided by a number of elements and s so I remember tea is one by

Joshua Eastwood · Answer

we have an experiment that&#x27;s going to toss a coin and then roll a die were legitimate, excited, fiery. But once the first of all to say That&#x27;s an eight, either ahead and then a one. I had a do ahead in it for me. I had in a four. I hadn&#x27;t if I were ahead. You&#x27;re getting the idea what I&#x27;m doing. And then you can also have all of those with hail. So tail on one ale into Elon three. Palin four Hailing five still in six total number. So what? You&#x27;re basically looking at it. Oh, so everything&#x27;s gonna be over. Find the probability of getting hand and an even number. Let&#x27;s look. And one that even had one undermined one. There&#x27;s still just 1/4 the 2nd 1 The second probability raft to find is the probability of getting a hand a number greater than four. And I&#x27;m just gonna write this greater than four means you can have a five or six. But that means I have what it produces 16 in the last part, asking for the problem of getting handles number. Okay, so, for, uh, I simply look at Palin on them at a total of all against 1/4

Ankit Gupta · Answer

Now we have experiment off. Those things are goin twice now in part, a venue to find our sample space. So sample spaces let samples Baswedan ordered by s so firstly for Tosa coin. Firstly, we get help Head tail anti No In a second dose we can get head, they&#x27;ll help they&#x27;ll. So there are four elements in sample space which are head head had tails Trailhead on building Now in part B, we need to select And even where we have two heads So named this even as e So this even where we have two heads is so they&#x27;re only one even where we can have to help which is at it Therefore, number off elements in even E is one on a number of elements in sambal space s our food Therefore probability that even Yorker&#x27;s or even the A curses one by food as the number of elements over number off elements in sample space Now in Park Si we need to select an event where we are getting at least one head. So let the letters name This even does f where we should have at least one help So one head isn&#x27;t had tail. Second outcome they&#x27;ll help also has one help on at least one else. So we can also have two heads. That is, this outcome can also be included in this event. So the total number off elements in even F is three. Therefore, probability that even after occurs, is number of elements in F over number of elements in samples piece which is three by food. So a probability that even f curses three by four. Lastly, in party, we need to find the probability off getting exactly one head. So let us named this even as J where we have exactly one hand. So we have one had in this outcome and this outcome, so H P and P it therefore are even has two elements. So number of elements and even JR to their number of elements and sample space were total four. So the probability that even Jay&#x27;s occurring is two by four that is one by two. So they are total off probably have total probability of one bite. So that even day occurs there we can have exactly one hand

Problem

For the experiments in Exercises 13–18, write out…

Problem 17 Easy Difficulty

Answer

(a) List outcomes of length $4 .$
$\{\text { HTHH, TTHH, THTH, HTTH, TTTH, TTHT, THTT, HTTTY. }$
(b) Outcomes with exactly $2 \mathrm{H} :$
$\{\mathrm{HH}, \mathrm{THH}, \mathrm{~ H T H , ~ T T H H , ~ T H T H , ~ H T T H \} . ~}$
(c) No heads-no "H' in the sequence:
$\{\text { TTTTT }\}$

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Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Finite Mathematics and Calculus with Applications

Grace H.

Catherine R.

Anna Marie V.

Samuel H.

Integration Review - Intro

Definite vs Indefinite

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(a) List outcomes of length $4 .$$\{\text { HTHH, TTHH, THTH, HTTH, TTTH, TTHT, THTT, HTTTY. }$(b) Outcomes with exactly $2 \mathrm{H} :$$\{\mathrm{HH}, \mathrm{THH}, \mathrm{~ H T H , ~ T T H H , ~ T H T H , ~ H T T H \} . ~}$(c) No heads-no "H' in the sequence:$\{\text { TTTTT }\}$

Finite Mathematics and Calculus with Applications

Grace H.

Catherine R.

Anna Marie V.

Samuel H.

Integration Review - Intro

Definite vs Indefinite

Margaret L. Lial, Raymond N. Greenwell, Nathan P. RitcheyFinite Mathematics and Calculus with Applications

Grace H.

Catherine R.

Anna Marie V.

Samuel H.

(a) List outcomes of length $4 .$
$\{\text { HTHH, TTHH, THTH, HTTH, TTTH, TTHT, THTT, HTTTY. }$
(b) Outcomes with exactly $2 \mathrm{H} :$
$\{\mathrm{HH}, \mathrm{THH}, \mathrm{~ H T H , ~ T T H H , ~ T H T H , ~ H T T H \} . ~}$
(c) No heads-no "H' in the sequence:
$\{\text { TTTTT }\}$

Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Finite Mathematics and Calculus with Applications