SOLUTION: A family has three children. Every child was born to be a boy or girl with 50% chance. The probability of this family having two boys is:

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Question 992094: A family has three children. Every child was born to be a boy or girl with 50% chance. The probability of this family having two boys is:
Found 2 solutions by Edwin McCravy, solver91311:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
The sample space of the orders of birth are

{BBB,BBG,BGB,BGG,GBB,GBG,GGB,GGG}

P(exactly 2 boys) = 3/8

P(at least 2 boys) = 4/8 = 1/2

Edwin
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

The sample space is:
    B  B  B   **
    B  B  G   *
    B  G  B   *
    B  G  G
    G  B  B   *
    G  B  G
    G  G  B
    G  G  G

There are eight possibilities. Three of the possibilities have two boys (*), and one has three boys (**).

So the probability of EXACTLY two boys is 3/8. The probability of AT LEAST two boys is 1/2. What the question means by "two boys" is a matter of interpretation. You choose which is the correct way to look at it. The sentence as written is ambiguous and could mean either exactly or at least.

John

My calculator said it, I believe it, that settles it

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