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Number of Siblings

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #38891 Fun: (2.35) Difficulty: (2.53) Category: Probability Submitted By: leftclick Corrected By: tsimkin

Ten-year-old Bert Sampson lives in the town of Springvale, where, out of all households:

2% include five children
7% include four children
14% include three children
31% include two children
16% include one child
30% do not include any children

What are the chances that Bert lives with two sisters and no brothers?

(Consider all children living in any given house as siblings).

6.646%

Since Bert is a child, he cannot possibly live in a household with no children. Therefore there is a (14*3)/(16+31*2+14*3+7*4+2*5), or 26.582% chance that he lives with two other children (i.e. in a household with three children).

There is a 50% chance that each of these other children is a girl, so there is a 25% chance that they are both girls.

Therefore, the total chance that Bert lives with two sisters is 25% of 26.582%, or 6.646%.

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