Test your Probability Knowledge, Answer provided.?

Question

Given:

The family has 6 children and one of them is a male

Question:
What is the probability that the family has 4 males and 2 females?

The answer is 5/21. Can anyone tell me how to get this answer using formula? (You shouldn't list all the possible combinations then count the number)

one of them is a male means at least one person is a male.

You dont know which one is male but you know one of them is male.

Answer 1

I assume that the given means that AT LEAST one of them is male. That exclude the possibility of 6 females.

There are 2^6 = 64 combinations, all equally likely, but one of them (6 females) is excluded. Therefore, there are 63 combinations left.

The number of combinations with 4 males and 2 females is 2 combinations out of 6 = 6 C 4 = (6*5)/(2*1) = 15.

The probability is therefore 15/63 = 5/21.

Answer 2

I came out with a slightly different answer.

Since one sex is fixed and the other five are unknowns, the question can be rephased there are five chidren. What is the probability that two are females:

Use binomial distribution:

f(k,n,p)= n!/[k!(n-k)!] (p^k) (1-p)^(n-k)

In this case k=2 (females), and n=5 (children)
If p=1/2 (not stated, but the probability of a female)

f(2,5,1/2)=5!/[2!(5-2)!] (1/2)^2 (1/2)^3
=(5x4x3x2)/[2(3x2)] (1/2)^5
=(5x2)(1/32)
=5/16

For the right p, you could get 5/21.

Answer 3

you are actually asking the probability of 3males and 2 females from 5 children since you know 1 is male.

Prob male = 1/2 ,prob female = 1/2 (or human race would dissolve!)

From binomial probability:

probability of 3 males and 3 females
= 5!/(3!*(5-3)!) * (1/2)^3 * (1/2)^(5-3)
=(5*4*3*2*1)/(3*2*1*2*1) * (1/2)^5
=(5*4)/(2*1) * (1/2)^5
=10 *( 1/32)
=5/16 (5/21 is wrong!)

Answer 4

You are preceding from a series of false premises. Let's establish them: False Premise #1: Science does not provide any "truths", only philosophies. Wrong. Science does not provide EITHER. Science provides FACTS. Rational, empirical, testable, falsifiable, observable facts. Your car does not run on philosophies...it runs because of scientific facts. The computer you used to make this post was not built with philosophies...it was built using scientific facts. False Premise #2: Facts are always the same thing as truths. Wrong. Envision this scenario:You are on a street corner when you look into a window and see two men talking. Suddenly, one pulls a gun from a holster and shoots the other. What just happened? The FACT is that one man has shot another, but what is the TRUTH behind the shooting? Facts and truths are dependent on the other, but they are often not the same thing. False Premise #3: There is something called called 'scientific atheism'. Wrong. Atheism is atheism, period. That most atheists utilize scientific inquiry and methodology as tools of understanding reality is no reason to suddenly create a false label. False Premise #4: Modern science is based on metaphysics and probability. Wrong. Metaphysics is NOT a branch of credible science...it is a branch of philosophy that deals primarily with relationships of matter and consciousness, especially on the ontological and cosmological level and is heavily connected to the more esoteric and abstruse branches of philosophy. Modern science is based on credible, empirical, observable, testable, falsifiable branches of science: physics, chemistry, biology, geology, astronomy, et. al. False Premise #5: Since science cannot currently explain how the forces that govern the universe came into being, science is really only a philosophy. Wrong. Science may not currently be able to understand how the governing forces of our universe came into existence, but so what? At one point in time, we didn't understand what caused diseases or what electricity is or how to cultivate the soil....but we eventually figured it out. Science is fluid and dynamic, always furthering it's knowledge and exploring today what it didn't understand yesterday. False Premise #6: Atheism is just about wanting to believe you are a god in your own mind. Wrong. Atheism is nothing more than a lack of belief in any type of god or deity. Trying to paint it as anything else is little more than intellectual dishonesty. By the way, try telling Buddhists and Taoists-who are followers of religions that happen to be atheistic-that they want to be gods. They'd laugh at you. False Premise #7: The only source of truth is the Christian 'god'. Irrelevant until established. Since no one has been able to provide any type of sufficient evidence for the existence of ANY god, the declaration "Truth is based on statements made by God Who has absolute knowledge" is meaningless. False Premise #8: Science is a philosophy. Wrong. Philosophy is a branch of human thought that deals with determining what constitutes and what value, if any, certain ideals have. Some of these ideals include justice, beauty, morality, love, etc. etc. Some philosophies address the question of existence and reality, which include material reality. However, such philosophies only question from the point of view of "why do these things exist?" and "where did they come from?" Science, on the other hand, does not ask any such questions. It is concerned, solely, with determining the what and why of how things work and how that knowledge can be utilized by man. It does not concern itself with abstracts such as beauty or ethics. It is concerned with what can observed, tested, falsified, verified and proven. It is, of course, possible to attach a philosophy to a scientific discipline, i.e., the philosophy of biology, and by extension create a system where one can discuss and incorporate philosophical ideals into a scientific discipline. However, science itself is not numbered amongst the philosophical disciplines. Before you continue with this argument, I suggest that you expand your knowledge on exactly what science is and how it works. I also suggest you develop a clearer understanding of what atheism is and what it is not. Although I'm fairly certain you are simply waiting for someone to agree with you, I hope you'll take this seriously.

Answer 5

meh.