Probability

Advika chooses one of three scarves every morning: Red, Blue, or Green.

• The probability she chooses Red is $20 \%$.





• The probability she chooses Blue is twice the probability of choosing Red.





• On the remaining days she wears a Green scarf.

Once a scarf is chosen, she decides whether to wear a Hat (H) and Sunglasses (S).

These choices are independent of each other but depend on the scarf colour:

$$ \begin{array}{|l|l|l|} \hline \text { Scarf colour } & \mathbf{P ( H )} & \mathbf{P ( S )} \\ \hline \text { Red } & 0.5 & 0.8 \\ \hline \text { Blue } & 0.4 & 0.5 \\ \hline \text { Green } & 0.1 & 0.5 \\ \hline \end{array} $$

Advika is spotted outdoors wearing both a Hat and Sunglasses.

What is the probability that she is wearing the Red scarf?