Children's Probabilities Challenge

Probability Level 3

A couple has two kids. One is a girl who was born on a Tuesday . What is the probability of the other one be a boy? (Assume that for any given pregnancy the respective probabilities that a male or female are conceived are the same. Assume that there is equally likehood to born in any day of the week)

14/27 2/3 1/3 1/2

1 solution

Pop Wong
Aug 17, 2020

Without the birthday information, the possible sample space will $\{ (G,G), (G,B), (B,G) \}$ and hence Pr(the other is a boy) $=\cfrac{2}{3}$

Take into account the birthday information,

$(G, G) \Rightarrow (G_i, G_j)$ where $i, j \in \{Mon, Tue, ..., Sun\}$

possible sample space $GG= \{ (G_{Tue}, G_j) , (G_i , G_{Tue}) \} |GG| = |(G_{Tue}, G_j)| + (G_i , G_{Tue}) - |(G_{Tue}, G_{Tue})| = 7+7-1=13$

$(B, G) \Rightarrow (B_i, G_{Tue})$ where $i \in \{Mon, Tue, ..., Sun\}$

possible sample space $BG = \{ (B_i, G_{Tue}) \}, |BG| = 7$

$(G, B) \Rightarrow (G_{Tue}, B_j)$ where $j \in \{Mon, Tue, ..., Sun\}$

possible sample space $GB = \{ (G_{Tue}, B_j) \}, |GB| = 7$

Probability $=\cfrac{\text{favorable outcome}}{\text{possible outcome}} = \cfrac{7+7}{7+7+13} = \cfrac{14}{27}$

Children's Probabilities Challenge

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