An engineering team is testing a new prototype drone. The drone has constant success rate of 2 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?

Step-by-step solution

Let p be the probability of a successful landing and q be the probability of a failed landing. p = 2 7 q = 1 - 2 7 = 5 7 Swarna attempts first, followed by Sarah. Sarah initiates the successful landing if the first success occurs on the 2nd, 4th, 6th, attempt. The probability of this happening is given by the sum of the probabilities of these mutually exclusive events: P( Sarah ) = qp + q^3p + q^5p + This is an infinite geometric progression with first term a = qp and common ratio r = q^2 . P( Sarah ) = qp 1 - q^2