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Then the girl may be visible. The first statement says that it can be either. While it is certainly true that every possible Mr.

Smith has at least one boy i. Smith with at least one boy is intended. That is, the problem statement does not say that having a boy is a sufficient condition for Mr.

Smith to be identified as having a boy this way. Smith, unlike the reader, is presumably aware of the sex of both of his children when making this statement", i.

If it is assumed that this information was obtained by looking at both children to see if there is at least one boy, the condition is both necessary and sufficient.

Three of the four equally probable events for a two-child family in the sample space above meet the condition, as in this table:.

However, if the family was first selected and then a random, true statement was made about the sex of one child in that family, whether or not both were considered, the correct way to calculate the conditional probability is not to count all of the cases that include a child with that sex.

Instead, one must consider only the probabilities where the statement will be made in each case. So, if at least one is a boy when the fact is chosen randomly, the probability that both are boys is.

The paradox occurs when it is not known how the statement "at least one is a boy" was generated. Either answer could be correct, based on what is assumed.

As Marks and Smith say, "This extreme assumption is never included in the presentation of the two-child problem, however, and is surely not what people have in mind when they present it.

Another way to analyse the ambiguity for question 2 is by making explicit the generative process all draws are independent.

Following classical probability arguments, we consider a large urn containing two children. We assume equal probability that either is a boy or a girl.

The three discernible cases are thus: 1. These are the prior probabilities. Using Bayes' Theorem , we find. The paradox arises because the second assumption is somewhat artificial, and when describing the problem in an actual setting things get a bit sticky.

Just how do we know that "at least" one is a boy? One description of the problem states that we look into a window, see only one child and it is a boy.

This sounds like the same assumption. However, this one is equivalent to "sampling" the distribution i. Let's call the statement "the sample is a boy" proposition "b".

Now we have:. The difference here is the P b , which is just the probability of drawing a boy from all possible cases i. The Bayesian analysis generalizes easily to the case in which we relax the population assumption.

If we have no information about the populations then we assume a "flat prior", i. Suppose one had wagered that Mr. Smith had two boys, and received fair odds.

Their wager will increase in value as good news arrives. What evidence would make them happier about their investment?

Learning that at least one child out of two is a boy, or learning that at least one child out of one is a boy?

The latter is a priori less likely, and therefore better news. That is why the two answers cannot be the same. Now for the numbers. If we bet on one child and win, the value of their investment has doubled.

Women share texts that show the VERY nasty ways 'nice guys' have turned on Superbike champion Sean Emmett 'throttled wife until she nearly passed out': Surrey detective tells inquest What is the secret behind herd immunity?

WFH IS less productive: One in four bosses claim staff working from home are less useful than when in the Drinkers flock to bars in Scotland for one last night out before Nicola Sturgeon's day Has the V-shaped recovery stalled?

UK economy grew by just 2. Big Brother is watching your social-distancing! Over 1, AI scanners are monitoring how close pedestrians Data shows the average age of death from coronavirus is Sir Keir Starmer accuses 'arrogant' government of a 'Whitehall knows best' handling of Covid crisis and Scotland fans cheer and chant while forced to watch team's tense victory over How close to the edge is the NHS?

Matt Hancock is accused of trying to 'bounce' Boris Johnson into shutting the hospitality sector after Europe divided by second lockdowns: Spanish PM holds emergency meeting to impose lockdown on Madrid as Europe's extra testing drives global coronavirus infections to the highest recorded level - but deaths China joins WHO-backed 'global coronavirus vaccine alliance' rejected by Donald Trump to ensure 'equitable WFH woes: Ten million homes were hit by bad broadband during lockdown as amount of people logging onto the

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Sophia 4. Jack 2. Aaron 3. Derik 4. Nate Nathan I hope that I helped! I actually really love that name. Dont change the spelling. Katherine Howell.

I love Juliet Grace How do you think about the answers? You can sign in to vote the answer. Juliet Grace is beautiful for real i love it i really like the name Scarlett and maybe the middle name Jane or Delaney maybe Rose for the middle name for the boy i love the name Frederick James I just like those names Congratulations!!!!!

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Show more answers 7. He says that several times between December and February, the suspects preyed on the victim — assaulting him with a knife, kicking him in the groin, dragging him by the hair, coercing him to engage in a sex act with an animal, and forcing him to walk on the partially frozen pond.

Bush, who lives in a rural part of the county south of Mechanicsville, knew the victim well, according to investigators.

Police say the girls have admitted to videotaping the incidents, but officials are still trying to figure out why.

It's hard to fathom, really. Both girls have been charged with two counts of 1st degree assault, two counts of 2nd degree assault, soliciting subject in the production of child pornography and false imprisonment.

Bush was charged as an adult. She is being held at the St. Mary's County Detention Center. The other teen is being detained at the Waxter's Children's Center.

Video: Two Maryland teens admit to assaulting boy with autism. Argos AO. Two teenage girls 'tortured mentally disabled boy, forced him to perform sex acts and recorded it all on their cell phones' Lauren Bush, 17 and another unnamed year-old recorded the assaults against the autistic year-old victim on their cell phones Footage shows them force him to walk on a partially frozen pond and they refuse to help when he falls through the ice several times Local sheriff described the harassment as among the most disturbing he had dealt with in his career Both girls have been charged with assault, soliciting subject in the production of child pornography and false imprisonment By Daily Mail Reporter Published: BST, 12 March Updated: BST, 12 March e-mail View comments.

Share this article Share. Read more: Two Maryland teens admit to assaulting boy with autism. Share or comment on this article: Chopticon High School teenage girls 'tortured boy, forced him to perform sex acts' e-mail.

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Women share texts that show the VERY nasty ways 'nice guys' have turned on Superbike champion Sean Emmett 'throttled wife until she nearly passed out': Surrey detective tells inquest What is the secret behind herd immunity?

WFH IS less productive: One in four bosses claim staff working from home are less useful than when in the Drinkers flock to bars in Scotland for one last night out before Nicola Sturgeon's day

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