COMEDK · Maths · 36. Probability
A company is migrating its database, and two software engineers, Ishaan and Kavya, take turns running a data-sync script that has a constant success rate of \(\dfrac{3}{8}\) per attempt. If Ishaan initiates the first attempt and they persist until the migration is successful, what is the probability that Kavya is the one who initiates the successful sync?
- A \(\dfrac{5}{13}\)
- B \(\dfrac{8}{13}\)
- C \(\dfrac{3}{11}\)
- D \(\dfrac{8}{11}\)
Answer & Solution
Correct Answer
(A) \(\dfrac{5}{13}\)
Step-by-step Solution
Detailed explanation
Let \(p\) be the probability of success and \(q\) be the probability of failure in a single attempt. \(p = \dfrac{3}{8}\), \(q = 1 - \dfrac{3}{8} = \dfrac{5}{8}\) Ishaan makes the 1st, 3rd, 5th, ... attempts. Kavya makes the 2nd, 4th, 6th, ... attempts. The probability that…
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