What Is the Probability of Having Exactly k Boys in a Family of n Children?

  • MHB
  • Thread starter evinda
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which takes into account the different combinations of births that could result in exactly $k$ boys.
  • #1
evinda
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MHB
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Hello! (Wave)

A couple gets $n$ children. At each birth, the probability to get a boy is $p$ (independent births). Which is the probability that exactly $k$ of the children are boys?

I have thought the following:

Let $X$ be the number of boys that the couple gets. Then the desired probality is

$P(X=k)=p^k \cdot (1-p)^{n-k}$

Am I right? (Thinking)
 
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  • #2
Hey evinda!

Yes, that is correct. (Nod)
 
  • #3
I like Serena said:
Hey evinda!

Yes, that is correct. (Nod)

Great! Thank you (Happy)
 
  • #4
evinda said:
Hello! (Wave)

A couple gets $n$ children. At each birth, the probability to get a boy is $p$ (independent births). Which is the probability that exactly $k$ of the children are boys?

I have thought the following:

Let $X$ be the number of boys that the couple gets. Then the desired probality is

$P(X=k)=p^k \cdot (1-p)^{n-k}$

Am I right? (Thinking)
Hello,

Your answer should be $P(X=k)=\binom{n}{k}p^k (1-p)^{n-k}$
 

FAQ: What Is the Probability of Having Exactly k Boys in a Family of n Children?

What is the meaning of "Exactly k children are boys"?

The phrase "Exactly k children are boys" means that out of a group of k children, all of them are boys and there are no girls in the group.

How is "k" determined in this statement?

The value of "k" in this statement is determined by the number of children in the group. For example, if there are 5 children in the group and all of them are boys, then k would be equal to 5.

What is the significance of stating "Exactly" in this statement?

The use of the word "Exactly" in this statement emphasizes the precision and accuracy of the statement. It indicates that there are no other possibilities or variations - only k children and all of them are boys.

Can "k" be any number?

Yes, "k" can be any number as long as it accurately represents the number of children in the group. It can be 0 if there are no children, or even a large number if there are many children in the group.

Is this statement based on scientific research?

No, this statement is not based on scientific research. It is simply a mathematical statement that describes a specific scenario where all k children in a group are boys.

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