SOLUTION: A family has 5 children. Assume that each child is as likely to be a boy as it is to be a girl. Find the probability that the family has 5 girls if it is known the family has at le

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A family has 5 children. Assume that each child is as likely to be a boy as it is to be a girl. Find the probability that the family has 5 girls if it is known the family has at le      Log On


   

Question 1157701: A family has 5 children. Assume that each child is as likely to be a boy as it is to be a girl. Find the probability that the family has 5 girls if it is known the family has at least one girl.
Answer by ikleyn(52786) About Me  (Show Source):
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Let represent any possible set of 5 children as a 5-letter world, consisting of letters G or B (G for a girl and B for a boy).


In all, 2%5E5 = 32 such words are possible, having 2 opportunity for each of 5 positions.


The condition "if it is known the family has at least one girl" means that we will consider the reduced space of all such words,
with the word (BBBBB) removed from the consideration.

This reduced space of events consists of 32-1 = 31 element.


The "favorable" set of events consists of only one such word  (GGGGG).


Therefore, the probability under the question is  P = 1%2F31.    ANSWER

Solved.