Class - boys and girls

In the class are 60% boys and 40% girls. Long hair has 10% boys and 80% girls.

a) What is the probability that a randomly chosen person has long hair?
b) The selected person has long hair. What is the probability that it is a girl?

Correct answer:

p₂ =  0.38
p₂ =  0.8421

Step-by-step explanation:

$$\begin{gathered} B=60\%=\frac{60}{100}=\frac{3}{5}=0.6 \\ G=40\%=\frac{40}{100}=\frac{2}{5}=0.4 \\ {l}_1=10\%=\frac{10}{100}=\frac{1}{10}=0.1 \\ {l}_2=80\%=\frac{80}{100}=\frac{4}{5}=0.8 \\ {p}_2=p_1=B\cdot l_1+G\cdot l_2=0.6\cdot 0.1+0.4\cdot 0.8=0.38 \end{gathered}$$

$p_2=\frac{G\cdot l_2}{p_1}=\frac{0.4\cdot 0.8}{0.38}=0.8421$

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