Consider a coin tossing game between Santa and Banta. Both of them toss two coins sequentially, first Santa tosses a coin then Banta and so on. Santa tosses a fair coin: Probability of heads is $1 / 2$ and probability of tails is $1 / 2$. Banta's coin probabilities depend on the outcome of Santa's toss. If Santa sees an outcome heads then Banta gets a coin whose probability of heads is $3 / 4$, and of tails is $1 / 4$. If Santa tosses a tail then Banta gets a coin whose probability of tossing a tails is $3 / 4$ and of heads is $1 / 4$.
What is the probability of the event that they both have one head and one tail in the two trials conducted by each of them?
- $1 / 2$
- $5 / 16$
- $3 / 16$
- $1 / 4$
- $1 / 3$