Probability problems are driving me crazy

[FatalExtracti0N]

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Can someone please help me understand this question :

What is the probability of having exactly 1 boy in a family planning for 3 children?

The question was from the QR of the first Achiever test and the answer was 3/8 but I didn't understand the explanation they provided. Thanks in advance for your help!

 

[loveoforganic]

There are 2 possibilities for each birth, male or female.

Therefore, there are (2)(2)(2) = 8 possible outcomes.

Since you want only one male child, that child could be born either first, second, or third. So 3 possibilities out of 8.

 

[Ibraiz]

There are 2 possibilities for each birth, male or female.

Therefore, there are (2)(2)(2) = 8 possible outcomes.

Since you want only one male child, that child could be born either first, second, or third. So 3 possibilities out of 8.

thanks for the great explanation lovefororganic. I was thinking more like this:

The probability of a boy from the first birth child would be 1/2 and the same for the second child 1/2 and the third 1/2 and we can multiply all of those to get the answer of 1/8.
1/2 x 1/2 x 1/2 = 1/8

Why can't we do this? and why is this method wrong?

 

[Chemwiz]

thanks for the great explanation lovefororganic. I was thinking more like this:

The probability of a boy from the first birth child would be 1/2 and the same for the second child 1/2 and the third 1/2 and we can multiply all of those to get the answer of 1/8.
1/2 x 1/2 x 1/2 = 1/8

Why can't we do this? and why is this method wrong?

that is correct, but you have to multiply 1/8 by 3 b/c son can be the 1st, 2nd, or 3rd child.