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Suppose that a study is being done on all families with one, two, or three children. Let the outcomes of the study be the genders of the children in descending order of their age.

A. List sample space: $M$ = Male $F$ = Female $$ \{M, F, MF, MM, FM, FF, MMM, MMF, MFM, MFF, FFF, FFM, FMF, FMM\} $$

B. Let $A$ be the event that the eldest child is a girl, and let $B$ be the event that exactly two children are girls. List the sample points in $A$ and $B$. Are $A$ and $B$ mutually exclusive? Why or why not?

Sample points $\{FF,FFM,FMF\}$

So they aren't mutually exclusive. But I don't know how to explain why or why not? Can somebody help me on this?

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  • $\begingroup$ Suspect they want you to first give the sample points in A & the sample points in B. In which case, after you answer "yes" to the question whether the sets are mutually exclusive, the following question, "why?", doesn't seem superfluous - just explain your reasoning in words as well as showing the intersection set. $\endgroup$
    – Scortchi ♦
    Commented Oct 20, 2014 at 9:18
  • $\begingroup$ Same homework problem as in this question posted 9 hours earlier. Unfortunately, this question cannot be closed as a duplicate because the other question does not have an answer as yet. $\endgroup$
    – Dilip Sarwate
    Commented Oct 20, 2014 at 13:17
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    $\begingroup$ Hint: A full and valid explanation would appeal to the definition of "mutually exclusive." What is that definition? $\endgroup$
    – whuber ♦
    Commented Oct 20, 2014 at 15:52

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They are not mutually exclusive because the intersection of A and B is not equal to the empty set

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