Samhita faces a three-headed dragon. She wins a "Tactical medal" if she manages to defeat exactly one of the three heads.

The battle proceeds head-by-head under the following conditions:

• The probability of defeating the first head is $\frac{\mathbf{1}}{\mathbf{3}}$.

• After a win: if she defeats a head, the probability of defeating the next head is $\frac{2}{3}$.

• After a loss: if she fails to defeat a head, the probability of defeating the next head is $\frac{\mathbf{1}}{\mathbf{4}}$.

What is the probability that Samhita earns the "Tactical medal"?

The odds against Arjun solving a problem are $\mathbf{5 : 2}$ and the odds in favour of Bhavana solving the same problem are 3:4. What is the probability that the problem is NOT solved by either of them?

A teacher has two jars of candy on her desk:

Jar 1: Contains 3 Strawberry candies and 2 Orange candies.

Jar 2: Contains 1 Strawberry candy and 4 Orange candies.

The teacher randomly picks two candies from Jar 1 and drops them into Jar 2.

Then, a student reaches into Jar 2 and picks two candies.

What is the probability that the student picks two Strawberry candies?

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?