An engineering team is testing a new prototype drone. The drone has constant success rate of $\frac{\mathbf{2}}{\mathbf{7}}$ for every autonomous landing attempt. Two engineers, Sarah and Swarna, take turns initiating the landing sequence, with Swarna going first.

If they continue the process until a landing is successful, what is the probability that Sarah is the one who initiates the successful landing?

Two numbers are selected at random from integers 1 to 9 . If their sum is even, what is the probability that both the numbers are odd?

If A and B are two events such that $P(\bar{A})=0.3, P(B)=0.4, P(A \cap \bar{B})=0.5$, then find the value of $P(B / A \cup \bar{B})$

In a game, a man wins ₹ 1000 if he gets an even number greater than or equal to 4 on a fair dice and loses ₹ 200 for getting any other number on the dice. If he decides to throw the dice until he wins or maximum of three times, then his expected gain/loss in (₹) is -----------