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Q#1 Probability GATE CH 2023 MCQ +2 marks -0.66 marks

An exhibition was held in a hall on 15 August 2022 between 3 PM and 4 PM during which any person was allowed to enter only once. Visitors who entered before 3:40 PM exited the hall exactly after 20 minutes from their time of entry. Visitors who entered at or after 3:40 PM, exited exactly at 4 PM. The probability distribution of the arrival time of any visitor is uniform between 3 PM and 4 PM. Two persons X and Y entered the exhibition hall independent of each other. Which one of the following values is the probability that their visits to the exhibition overlapped with each other?

\(\frac{5}{9}\)

\(\frac{4}{9}\)

\(\frac{2}{9}\)

\(\frac{7}{9}\)

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