Answer :
The conditional probability formula is given as
[tex]P(HH|C)=\frac{P(HH\cap C)}{P(C)}[/tex]where
[tex]P(HH\cap C)[/tex]denotes the probability of the intersection zone.
From the given picture, we can note that the number of elements in each of the above zones are:
[tex]\begin{gathered} n(HH\cap C)=4 \\ \text{and} \\ n(C)=10 \end{gathered}[/tex]Then, we have
[tex]P(HH|C)=\frac{P(HH\cap C)}{P(C)}=\frac{4}{10}[/tex]by symplifing this result, we have
[tex]P(HH|C)=\frac{2}{5}[/tex]