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

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 committee of 2 people is selected at random from 5 executives: Alam, Bartolini, Chinn, Dickson, and Ellsberg.
a. Chinn is on the committee.
b. Dickson and Ellsberg are not both on the committee.
c. Both Alam and Chinn are on the committee.

Amy Jiang · Accepted 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.

Amy Jiang · 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

Lourence Gonhovi · Answer

all right. The experiment is conducted for which the symbol spaces giving well, you have a phone line. Probability is more simple. If in experiments. Impossible then that said, just what? This experiment is not possible just apparently because of the negative point as they ate, uh, they were always in Wiseman possible. It&#x27;s this member. The probability distributions should like to know one end between Sarah and one and any other interval is no exception. Outside that individual more mumbles that certain probability distribution.

Lourence Gonhovi · Answer

All right. So if you look at this experiment one to check whether it is a possible experiment Eso There&#x27;s little point, uh, is that all mine glass. So don&#x27;t win 32 and something to on. But it&#x27;s true. A glass last time you five glass settle brain 13 All right, so if you add all this, you get one. Which then is that despise the one of the requirements for improbably to distribution that all the probability density and them you get one.

Lourence Gonhovi · Answer

all right. In this experiment, the numbers as 0.9 to 0.3 Settle point Mine too. Last 0.3 blouse, sandal and so open. So set up pointing to settle two plus little pins. Little three again. Now, if we&#x27;re going to add this, uh, we get, um, one. So since we are getting a one, it means that the condition has been met You that the probability distribution some should always be equal to one. So this assignment is possible.

Lourence Gonhovi · Answer

an experiment is conducted for which the simple Spence is s. Which of the full improbability assigned mates are possible for this experiment there, Sandman. And it&#x27;s not possible to know why. So this is one of 314161 of our aid. 2010. So we have to edit check. All right, so if we end this, we will get funding, but leave last one month for seats. Last one of age. That&#x27;s one of 10. We get a little 0.975 So this is not possible because we want a some for the probability distribution to be able to mind. So this is the last time before one. So this is less than that. Settle point names, and in fact, so the experiment is impossible.

Problem

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

Problem 13 Medium Difficulty

Answer

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