Out that these 4 outcomes, $3$ room favorable. So the probability must be $\frac34$.

You are watching: What is the probability of having 3 children that are all boys?

But should you take right into account the order of your birth? since in that situation it would be $\frac78$!


*

*

The match of at least one boy is all 3 girls

So, $P($ at least one boy$)=1-P(GGG)$

$=\displaystyle1-\left(\frac12\right)^3$

This is the de facto way of solving troubles of Probability the at the very least one in situation of Binomial distribution like tossing a coin etc.


*

There room in fact eight possible outcomes:

$$GGG\,,\,GGB\,,\,GBG\,,\,BGG\,,\,BBB\,,\,BBG\,,\,BGB\,,\,GBB$$

Of these, just one go not include a young (B) in the event, and also thus the probability of all girls is $\;\dfrac18\;$ .


*

Another method to look in ~ this is to attract this out

*

Here i follow the stereotypical association of gender and colors: the blue boxes represent boys and the pink boxes stand for girls. Every time you have actually a boy or a girl, in the next generation you can have a boy or a girl also, for this reason the number of possibilities is doubled every generation.

In terms of your problem, once you have actually a boy, that represents a checkmark versus "at least one of lock is a boy", so I"ve crossed package concerned. However all the succeeding generations after this young are additionally families in which there is at least one boy, for this reason I"ve overcome those out too. You have the right to see the the opportunity of having actually at the very least one young is $1/2$ in the very first generation, $3/4$ in the second, and also $7/8$ in the third. This generalizes to $(2^n-1)/2^n$ in the nth generation.

Conversely the opportunity of having no guys is $1/2$ in the an initial generation, $1/4$ in the second, and $1/8$ in the third. This generalizes come $1/2^n$ in the nth generation.

See more: Use As System Photo Library Greyed Out When Trying To Import

(Essentially I"ve attracted a probability tree chart here, which generalizes to lot more facility problems).