Problem 3. Tom has one sibling. What is the probability that he has a sister.

6 Answers

aespinoza71's profile pic

aespinoza71 | (Level 1) Adjunct Educator

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There is mathematical answer, and there is also a real-life answer.

It could be dependent on how old Tom's sibling is.  According to the U.S. Department of Labor, newborn boys outnumber girls 51% to 49%.

However, over the longitude of time, that number changes.  According to the U.S. Census Bureau, boys outnumber girls in youth.  As the population ages, females begin to outnumber men around the age of 35-40.  This holds true for both the U. S. and the world in general.

However, with the population growth, and the number of younger people in this world, currently, males make up 50.35% of the world population.  

So, based on this information, I would contend that Tom's sibling is more likely to be male.  


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billdelaney's profile pic

William Delaney | (Level 3) Distinguished Educator

Posted on

This is an excellent answer. 

Is there any such thing as a greater probability that a man who sires a son or a daughter will sire a second, and even a third and fourth, child of the same sex. It seems that there are couples who have nothing but boys or nothing but girls.

Is this always just a matter of pure chance? Or is there something in the father's genetic makeup that produces faster and stronger spermatazoa of one kind or the other? On the other hand, is there something in the mother's genetic makeup that rejects spermatazoa of one sex or the other? If so, the probability of the second sibling in this scenario being a boy would be greater than fifty or fifty-one percent.

Also, it is well known that in some countries they favor boys and abort girl fetuses. 

embizze's profile pic

embizze | High School Teacher | (Level 2) Educator Emeritus

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If this question had asked the probability of a pair of siblings having a girl if one of the siblings is known to be a boy then the answer would be 2/3. This is because the possibilities are BB,BG, or GB.

However, this question specifically points out one of the siblings.

Now Tom can be the older sibling or the younger sibling. If the older, he can have a younger brother or a younger sister. If he is the younger sibling, he can have an older brother or an older sister. Let T be Tom, B be a brother and S be a sister. The order of the pairs is the birth order:

The possibilities are (T,B),(T,S),(B,T),(S,T). There are 4 cases, two of which have a female sibling, so the correct answer is indeed 1/2.

The reason for the difference is that there are now 2 different cases of two boys. If M is male and F female, we do not have MM,MF,FM,FF. Instead we have Mm,mM,MF,FM where M,m and m,M are the different cases of whether Tom is older or younger.

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embizze's profile pic

embizze | High School Teacher | (Level 2) Educator Emeritus

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Here is another way to think of this:

(1) Suppose you flip two indistinguishable coins and you are told that one of the coins is heads. Then the probability that the other coin is tails is 2/3 as the possibilities were HH,HT,TH.

(2) Suppose we flip a quarter and a dime. You are told that the quarter is heads. Then the probability that the dime is tails is 1/2. This corresponds to the actual question as Tom is distinguishable from the other male.

qHdH,qHdT,qTdH,qTdT are the only possibilities and only the first two have quarter heads. This is different from HH,HT,TH,TT because now the coins would be indistinguishable.

malkaam's profile pic

malkaam | Student, Undergraduate | (Level 1) Valedictorian

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This question can be related to that of a coin, a coin has 2 sides, therefore it's probability is 0.2, in the same way there are 2 genders (male or female) so it can either be one or the other therefore it's probability is also 0.2.

The possible outcomes are (M,F),(M,M). Where M stands for Male and F stands for Female.

steamgirl's profile pic

steamgirl | Student, College Junior | (Level 1) Honors

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Probability questions can be broken up into 2 steps:

First, how many possible outcomes could there be. In this situation, there are 2 possible outcomes, either Tom has a brother or a sister since he only has one sibling. This makes up the denominator of your probability ratio.

Second, determine how many chances are possible for the asked situation to happen (example: 3 red marbles, 2 blue = 3 chances to pull red). In this case there is only one chance that Tom has a sister, this makes up the numerator of your probability ratio. 

Therefore, the probability of Tom having a sister is 1/2, or 50%.

xtaq's profile pic

xtaq | Elementary School Teacher | (Level 1) eNoter

Posted on

Its pretty simple since theres only 2 type of genders (Male and Female) so the probability is 1 of 2.

nisarg's profile pic

nisarg | Student, Grade 11 | (Level 1) Valedictorian

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it levels out to around 1/2 because the other child can be either a girl or a boy.