From the 8 outcomes, 4 (BBB, BBG, GBB, GBG) are outcomes that involve having a boy as the 2nd child. From this list, ONLY 1 will be EXACTLY 1 boy,

with the 2nd child being a boy (GBG). Therefore, 

OR

Use the CONDITIONAL FORMULA:  



                             P(1 BOY|2nd is a BOY) =  = 

I don't know why that person thought this problem was incomplete. I don't know what he's looking at.

The other person, I don't know what she was thinking either, with an answer of 3/8. They BOTH don't make any sense!! 

Answer by ikleyn(52890)   (Show Source): You can put this solution on YOUR website!
 .





            The problem can be solved by various ways.







Solution 1.    Make and use the sample space directly and explicitly.





The sample space is 

    BBB  BBG  BGB  BGG  GBB  GBG  GGB  GGG

(by coding B = boy,  G = girl).


All outcomes are equally likely with the probability of   =   each.


The number of outcomes with a boy as a second child is 4  (BBB  BBG  GBB  GBG).

Of them,  the number of outcomes with only one boy in the family is 1 (GBG).


Hence, the probability under the question is  P = .






Solution 2.    Logical analysis.





If the boy (B) is in the 2-nd  of the 3 positions, then for the 1-st and for 3-rd position only  G  is possible.

Each G at the 1-st position and each G at the 3-rd position goes with the probability of .

Hence, the probability to have  G  at  the 1-st and 3-rd positions, under the condition, that the 2-nd position is B, is   = .




In both solutions, you have the same ANSWER :





          the probability under the question is  .
------------





Solved, answered, and explained.





 

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