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Acouple has four children. Assuming independence and thal (he probability of a boy is 2 determine the probability that the oldest child is boy and the three younges...

Question

Acouple has four children. Assuming independence and thal (he probability of a boy is 2 determine the probability that the oldest child is boy and the three youngest children are girlsThe probability is (Type an integer or a simplified fraction:)

Acouple has four children. Assuming independence and thal (he probability of a boy is 2 determine the probability that the oldest child is boy and the three youngest children are girls The probability is (Type an integer or a simplified fraction:)



Answers

Suppose a family has 5 children. Suppose also that the probability of having a girl is $\frac{1}{2}$ Find the probability that the family has the following children. At least 3 boys

According to the equation, probably be off goal is equal to one way, too, so probably deals. Boy would also be equal to one. By do the number of skills of the family has is equal to fight for to the you boys on Google's, we would have to choose to out of the five independent birds, so that required probably D required probability is equal to five c We're choosing to out of the five independent birds. Probably the awful Goal Jail Square and probably deal for boy J Q. So if I see you will be 10 into one upon to hold square into one upon to hold you so 10 upon four into it. This would give us five a born 16 so this is the required probability.

In discussion, it is told that there is a family of two Children and it is told that at least one of them is boy. So if we want to write the simple space of this condition, that is at least one of them is a boy, then we can write it as a boy. Girl. Second one is girl boy and the third one is both boy. So these three possibilities are there. If you talk about at least one of them is boy. Now it is told that what is the probability of both boys? So you can see that there are total three possibilities. So we have to divide by the total with the favorable. You can see that the favorable is this case That is one and the total are The three cases. So we have to divide by three. So I can say that the answer for this question is one, divide by three. This is the answer of this question. Okay, thank you.

According to question, the probability of a goal is equal to one by two. So obviously the probability of a boy would also be equal to one by two, since the total of them should be one. Now the family has five kids on. We have to calculate the probability of the family having exactly, exactly to the Eagles. I'm two boys. So the required probability would be Robbie ability. It would be five c three. Since we're choosing three out of the five independent birds. Probably be off goal in to hold you and probably the oh boy, whole square. So five seats we would be then van a porn toe que into one upon two square so this would give us then upon it in due for so five upon 16. So this is the required probably

Okay, This question asks us probability of having at least five boys from a group of five Children assuming equal chances for each gender. So to find the probability of at least three, well, that can happen if we have three boys or if we have floor or if we have five, and we can just add these probabilities together because they're mutually exclusive. So now we'll just use the binomial distribution to find each of these, although we don't have to do it for T of five, because there's only one way that can happen, so we can just use a short cut on that one. But for P of three, it's five Children choosing three to be boys times the probability to get a boy, and we want three of them. And then that means that the other two Children are girls. And then next one, we have five Children picking four to be boys times the chance to be a boy to the fourth power times the remaining child, which is a girl. And then we add the probability of getting five boys, which is just that 1/2 chance happening five times in a row, so Now let's simplify. So we have five Choose three, which using our calculator for that five shoes. Three is 10. So this is tend about by 32 then five. Choose Force five suite of 5/32 and then we have a 1/32 so again were adding P three plus before, plus P five. And that's 16/32 which is 1/2 and that's our probability.


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