5 answers

Refer to the previous exercise. If at each stage the person who currently "has" the rumor does not know who

Question:

Refer to the previous exercise. If at each stage the person who currently "has" the rumor does not know who has already heard it and selects the next recipient at random from all five possible individuals, what is the probability that Fhas still not heard the rumor after it has been told ten times at the party?


Answers

Refer to the previous exercise. If at each stage the person who currently "has" the rumor does not know who has already heard it and selects the next recipient at random from all five possible individuals, what is the probability that Fhas still not heard the rumor after it has been told ten times at the party?

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Whether in this problem, we are asked to use orders method to approximate end of three for this differential equation. D N d t were given equals zero point through too. Time is 500 minus in times end of the 1/2 were also given that in the beginning only two people have heard the rumor. So that means end of zero equals two R h value is given to be 0.5 and we've got to find approximation for end of three. All right, so we will begin, make a little chart for ourselves at each step will need our time.

You will need r N value at that time. Uh, the book always calls this function here g so on the g of Are tee and their end. Of course, it'll only dependent. And in this case we'll take that result in each step and multiply by H, which is 0.5 and then finally, for orders method mean toe. Add that to our current and value, and that will give us our next and value, and we'll just keep repeating that.

So let's start with our initial condition and zero equals two means that when t zero and is too. And in fact, we know the rest of the T values because H is 0.5. So we just keep adding 0.5 until we get to three. Okay, we're ready to go. So in this first row, will those plug in to for N into that function? G up there.

And when we do, make sure that we get 14.856 Multiply that by 0.5 to give us 7.4 to 8. Add that to our current Y value of two and we'll get 9.4 two, eight. So let's copy that down. And now we plug this new value into Theo equation above her function G. And that will give us 29.52 74 times 0.5 gives us 14.7637 Add that to our current y value and we get 23.8065 which we copy into the next room.

Okay, that we take that and put it into G. We'll get 46.46 feet seven times 0.5 gives us 23.2344 Add that to our current in value to get 47. So for eight. Okay, that's our new N value. So at this 0.47 people, I have heard the rumor.

All right, we input that in too. Um G and will get 62.1336 times 1/2 31.668 And at that to end to get 78.107 six. We're getting there. Plug that in and we get this times 1/2 37.286 to just make sure your calculations match with these, if any of them. Don't you know exactly where to double? Check your work? All right, so we're near the end here, our second class.

Why value? We have put that in for Gene and we get a 2.63 times 1/2 will give us 41.35 And finally add that to our current y value to get 156.709 Copy that down here. And when is we'll round up to the nearest person? So 157 that is Oilers methods approximation for end of three. And we're done. Hopefully this hope.

Okay, so there is a circle five course fans apart. A What is the probability that the rumors repeated in the order B C E? Well, if the first person who's told the rumor that's one over for a chance and then once distressing this tote, this one less person. So it's one of before Here's what, over three years to splint and this is his point. Still, no e three for a party. Uh, what is the probability that F the third person in party told of the rover? So the first person has gents.

1/5 chance, they told the second person, has a 1/4 and then f being the good person in a party told the rumor is just one over the right not to go to 0.167 Robert C. What is that? What is the probability that F is the last person to hear? That's the same adjust ability because it was last year to appoint zone, so it's.

So, for part a the law of total probability gives us that property of L is equal to the sum of problems. Come over. I will probably isa bye times. Probably l given Isa bye. And so this is 0.40 times 0.2 plus 0.5 times point no.

One plus 0.1 times 0.5 which is 0.18 Well, for part B, we have the property of you. One compliment given l compliment is equal to one minus the property of E one, given alcohol, which is one minus the probability of you want intersect. L compliment, divided by the probability of l compliment, which is one minus. The probability of you won times the probably of l one or L compliment given you one divided by one minus property of a L. Just one minus 10.4 times 0.98 divided by one minus 10.18 It is equal to 0.601.

Get a report? A. Our solution is just B Y o pichichi vehicles. Okay. Why one minus y now for part it be we're giving that. We need to find kids assuming that 10% of the population was the rumor at time T So why g? We have put four our 0.1, which is started wiser.

Always a good 0.1 just 10% in it. Why do we have that would support before, which is 40% of the population knows to waste on this? We are based in part. They are general solution is why t isn't good. Hey, which is one over one minus e. You don't make a change t oversee.

And we know that. Why, Joe is you would support one to put one in you too. One What is one over one over one ways. E. Zoe's one oversee so it.

Yet it's all frisky. 2.1. My next. Put one over. Seek make one.

Subtract points. One beside you. Get nine. Good. Negative 0.1.

See what? Nine. She is too negative. Put one musical 2.1 over 0.9. What is that? When I live quite one divided by 0.9. It's also this one overnight.

So yet cuz equal to negative one overnight looking that I can to our solution you get why t physical too went over one bite make it okay to you and C is negative one overnight. That's this personally okay. And we also have that wide too is equal to point for us. So we have points for that one over one plus nine e t a bigger k times t which is to Okay, now we can solve for Kay. So we get 0.4 plus nine times 90.4 just 3.6 e in the negative to kay is equal to one subtracting 10.1 point.

Foreign books. I'd get one minus 24. Just 0.6 is equal to 3.6. Excuse me. Easy need to Okay.

You know, dividing by 3.6 on both sides that he got to Okay, since he quit 2.6 over 3.6. Taking Alan or both sides you get native to K is you go to a lot of 0.6 over 3.6 divided by native to when we get K is equal to this thing over here. So let's put that into our Captain Vetter. So, Ellen, a plate 6 to 1 of the 3.6. I wonder if I'm a good too.

This week A is equal to 0.895 It's 79735 Okay, so are Y o t physical to one over one plus nine e t o negative cane. It is negative point. It's 95 It's 79735 g. All right for part C were asked to, Let's see, assuming using our assumptions of part being determined 1 75% of the population with no turnover. Okay, so that's this wife T is equal to 75% which is 750.75 So we just sent this offer tea.

So we get 0.75 is equal to one over one plus nine. Your point, spades. 95879 735 t. It's more supplied by one person. I need to have this whole thing get 0.75 plus 9 1756.75 You too.

Negative. 0.8 nine. Thought that Thought T is equal to one. It's attracting 10.75 Both sides get one minus 10.75 Just 2.25 is equal to 6.75 Each of the negative points eights 95 It's seven 97 You know, we just divide by 6.75 and take Eleanor both sides. We get Dylan.

What you find over 6 27 5 is equal to *** points. It's 9579735 t the body where it is holding I'm o. It's like I have 8797 35. Okay, let's put this into fine T. If you plug this into your calculator, you get that T is equal to 3.67 It's it's days..

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