Question

Here, the sample space is a list of all the possible combinations of boys and girls for a family with three children. Because the probability that a child is a boy and the probability that a child is a girl are equal, all the outcomes are equally likely. Let M represent a boy (male) and F represent a girl (female). Then, for example, MMM represents the outcome where all three children are boys. FFF represents the outcome where all three children are girls. So, two of the events are MMM and FFF. The other events will consist of the ways that some children are girls and some are boys. (b) What is the probability that all 3 children are male? Notice that the complement of the event "all three children are male" is "at least one of the children is female." Use this information to compute the probability that at least one child is female. We will first find the probability that all three children are male. Recall that the probability of an event is given by the following. probability of event = number of favorable outcomes total number of outcomes In part (a), we found all the equally likely outcomes for the family. They are MMM, MMF, MFM, MFF, FMM, FMF, FFM, and FFF. Therefore, we see there are total outcomes possible for the family. Of these total outcomes, is/are favorable to the outcome "all three children are male." We use these values to calculate the probability as a fraction. P(all three children are male) = number of outcomes where all three children are male total number of possible outcomes = first child second child third child Event boy boy boy MMM boy boy girl MMF MMF boy girl boy MFM boy girl girl girl MFF girl boy boy FMM FMM girl boy boy girl FMF FMF girl girl boy FFM girl girl girl FFF

          Here, the sample space is a list of all the possible
combinations of boys and girls for a family with three children.
Because the probability that a child is a boy and the probability
that a child is a girl are equal, all the outcomes are equally
likely.
Let M represent a boy (male)
and F represent a girl (female). Then, for
example, MMM represents the outcome where all
three children are boys. FFF represents the
outcome where all three children are girls. So, two of the events
are MMM and FFF. The other events
will consist of the ways that some children are girls and some are
boys.
(b) What is the probability that all 3 children are male? Notice
that the complement of the event "all three children are male" is
"at least one of the children is female." Use this information to
compute the probability that at least one child is female.
We will first find the probability that all three children are
male. Recall that the probability of an event is given by the
following.
probability of event = 
number of favorable outcomes
total number of outcomes
In part (a), we found all the equally likely outcomes for the
family. They
are MMM, MMF, MFM, MFF, FMM, FMF, FFM,
and FFF. Therefore, we see there
are   total
outcomes possible for the family. Of these total
outcomes,   is/are
favorable to the outcome "all three children are male." We use
these values to calculate the probability as a fraction.
P(all three children are male)
  =  
number of outcomes where all three children are male
total number of possible outcomes
 = 
first child
second child
third child
Event
boy
boy
boy
MMM
boy
boy
girl
MMF   
MMF
boy
girl
boy
MFM
boy
girl
girl   
girl
MFF
girl
boy
boy
FMM   
FMM
girl
boy   
boy
girl
FMF   
FMF
girl
girl
boy
FFM
girl
girl
girl
FFF

Added by Michael N.

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