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February 16th, 2014, 03:57 AM   #1
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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
Abstract3000 is offline  
February 16th, 2014, 12:25 PM   #2
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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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