a woman has 5 children. 2 girls born first, then 3 boys followed. What is the probability that child number 6 will be a girl? A boy?

Question

 a woman has 5 children. 2 girls born first, then 3 boys followed. What are the odds that child number 6 will be a girl? A boy?

Answer 1

Probability is defined as  (number of successful outcomes) / (number of possible outcomes).  "Odds" are written as:

    successes :possibilities

 

For child number 6 (or for any other child), the probability is 1/2, the odds are 1:1 (note: this is biology and is not totally uniformly random, but this is a math/statistics problem).  It does not matter what previous children have been born; this one has a 50-50 chance, 1:1 odds, 50% probability of being a girl.  Same (actually, 1 minus that) for being a boy.

Answer 2

Assuming all the births are independent and a boy or girl is equally likely the odds are 1:1.