Answer
a) see table below
b) $\frac{3}{10}$
c) $\frac{5}{9}$
d) The probability of no left-handed family member given that the person is left-handed is $\frac{5}{9}$.
Work Step by Step
a) The accomplished table is shown below.
b) Since there are $3$ left-handed people out of the $10$ people who were surveyed, then
$$
P(\text{left-handed})=\frac{3}{10}
.$$
c) Using conditional probability then
$$\begin{aligned}
P(\text{no left-handed|left-handed})&=\frac{\frac{1}{3}\cdot\frac{1}{2}}{\frac{3}{10}}
\\&=
\frac{1}{6}\div\frac{3}{10}
\\&=
\frac{1}{6}\cdot\frac{10}{3}
\\&=
\frac{5}{9}
.\end{aligned}$$
d) The probability of no left-handed family member given that the person is left-handed is $\frac{5}{9}$.
