What is the probability that a person has both of these attributes? The probability that a blue-eyed person is left-handed is $\frac{1}{7}$.
The probability that a left-handed person is blue-eyed is $\frac{1}{3}$ . 
The probability that a person has neither of the attributes is $\frac{4}{5}$. 
What is the probability that a person has both attributes?
I just don't know how they got the answer
Answer: $\frac{1}{45}$

Draw a Venn diagram!
Let probabilities be as follows:
$a$=Blue only
$b$=Blue and Left
$c$=Left only
$d$=None
From probabilities given, 
$$\begin{align}
\frac b{a+b}=\frac 17 \quad \Rightarrow a&=6b\\
\frac b{b+c}=\frac 13 \quad \Rightarrow c&=2b\\
d&=\frac 45\\
\end{align}$$
As the probabilites sum to 1, 
$$\begin{align}
a+b+c+d&=1\\
6b+b+2b+\frac 45&=1\\
9b&=\frac 15\\
b&=\frac 1{45}\end{align}$$
