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So there are four groups. You survey the groups and count how many boys are in the group and girls are in the group. $$\begin{matrix} & \text{Boy}& \text{Girl}& \\\text{Group A} & 37 & 0 \\ \text{Group B} & 153 & 31 \\ \text{Group C} & 73 & 17 \\ \text{Group D} & 19 & 7\end{matrix}$$

Now, suppose that you sample a random person from all groups, and find that the person is from Group C. How can I calculate the probability that the person is a girl?

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    Have you considered drawing a tree diagram? It would really be useful here. – 2017-02-07
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    @Oliver821 No, I haven't. How would that help? – 2017-02-07
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    By drawing one you can clearly see the probabilities of choosing a group and if it's either a boy or a girl. By the way, do group A,B,C,D have a $\frac {1}{4}$ chance of being chosen? – 2017-02-07
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    @Oliver821 I slightly changed the problem. – 2017-02-07
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    What we have here is what's called a conditional probability problem. Have you worked with them before? The edit made this problem much clearer. – 2017-02-07
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    @Oliver821 I have, but I can't really piece things together properly. – 2017-02-07
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    By 'sample a random person from all groups' I guess you mean that each of the 337 (if I added correctly) children had an equal chance to be chosen. Then $P(Girl | Gp C) = 17/(73+17).$ No 'tree diagrams' necessary. No 'piecing things together'. Once you know it's Gp C you are interested only in the 'reduced population' of 90 people in Gp C. – 2017-02-07

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