Question 1130938
Let X denote the number of girls in a family with four children. Calculate P(X ≥ 3). 

I honestly don't even know where to begin with this.
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They want the probability that the number of girls is 3 or 4 in a family of four children:<br>

{{{ P(X>=3) = P(X=3) + P(X=4) }}}<br>

{{{ P(X=3) = (1/2)^3(1/2)(4C1) = 4/16 = 1/4 }}}
{{{P(X=4) = (1/2)^4 = 1/16 }}}<br>

{{{ P(X>=3) = 4/16 + 1/16 = highlight( 5/16 ) }}}<br>

To verify, we can enumerate all possible Boy/Girl families of four children:<br>

BBBB
BBBG
BBGB
BBGG
BGBB
BGBG
BGGB
{{{green(BGGG)}}}

GBBB
GBBG
GBGB
{{{green(GBGG)}}}
GGBB
{{{green(GGBG)}}}
{{{green(GGGB)}}}   
{{{red(GGGG)}}}