A couple decides to have children until they have one boy and one girl, but they will not have more than three children. Choose the correct sample space for this random experiment.
$S=\{G G G, G G B, G B G, G B B, B B B, B B G, B G B, B G G\}$
$\mathrm{S}=\{\mathrm{GGG}, \mathrm{GGB}, \mathrm{BBB}, \mathrm{BGG}\}$
$S=\{G B, B G, B B G, G G B\}$
$S=\{G B, B G, B B G, G G B, B B B, G G G\}$
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Answer
\(\boxed{S=\{G B, B G, B B G, G G B\}}\)
Step 1 ：A couple decides to have children until they have one boy and one girl, but they will not have more than three children. Choose the correct sample space for this random experiment.
Step 2 ：The possible outcomes are: having a girl then a boy (GB), having a boy then a girl (BG), having two boys then a girl (BBG), and having two girls then a boy (GGB).
Step 3 ：So, the correct sample space for this random experiment is \(S=\{G B, B G, B B G, G G B\}\).
Step 4 ：\(\boxed{S=\{G B, B G, B B G, G G B\}}\)
