IIT JEE , AIEEE Forum - Mathematics , Algebra

sprinkle

Suppose t is the time (in minute) and t = 0 at 11 am and t = 60 at 12 noon.

(assuming persons may arrive at any time between 11 and 12 with equal probabilities)

Now consider the 3 cases:
Case. 1. if first one arrives between t = 0 and t = 20 (say at t = t) then:

they can meet only if second person reaches between t = 0 and t = t + 20

suppose first person reaches after t = t min and dt is the infinitesimal interval of time when he arrives.
probability that first person reaches in dt time interval = dt/60
probability that second person comes between t = t and t = t + 20 is (t+20)/60

=> probability of meeting = ₀

²⁰ (dt/60) ((t + 20)/60) = 1/6

Case 2. if first person arrives between t = 20 to t = 40 then they will meet if second person comes within 40 min interval (20 min before and 20 min after that exact time when first person reached).

=> probability of meeting = 20/60 * 40/60 = 2/9

Case 3. if first person arrives between t = 40 to t = 60 (say at t = t) then they will meet if second person comes between t = t - 20 and t = 60
(similar to case 1.)
=> probability of meeting = 1/6

All 3 cases described above are mutually exclusive cases.

=> total probability = 1/6 + 2/9 + 1/6 = 5/9 ANS

sorry for any calculation mistake!

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