My Math Forum Help with Solving Independent events

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 February 16th, 2014, 03:57 AM #1 Newbie   Joined: Feb 2014 Posts: 9 Thanks: 0 Help with Solving Independent events Ok so I have the following problem I'm stuck midway through trying to figure out what exactly to with the numbers. refer to a family with four children. Assume that it is equally probable for a boy or a girl to be born. what is the probability of at least one boy and at least one girl given that there is at least one girl? I think this is supposed to be P(E intersect F) = P(E)P(F) The first part is that if there has to be at least one boy and one girl that leaves out (bbbb) & (gggg) from our sample space of 16 therefore giving me (14/16) Now when looking at the 2nd part "given there is at least 1 girl" removes (bbbb) from the sample space leaving me with (15/16) So am I multiplying these numbers together? or am I completely off track with this problem? Thanks for the help
 February 16th, 2014, 12:25 PM #2 Global Moderator   Joined: May 2007 Posts: 6,613 Thanks: 617 Re: Help with Solving Independent events There are 15 possibilities with at least one girl. There is one possibility (out of 15) with no boys. Your answer is then 14/15 for the probability of at least one boy.

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### a family with four children is referenced. assume that it is equally probable for a boy or a girl to be born. what is the probability of exactly two girls?

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