Question

MATH REASON OF PROBABILITY

Sonia and Natasha are supposed to meet at a certain location around 5:30 pm. Sonia arrives at some time uniformly distributed between 5:00 pm and 6:00 pm, while Natasha arrives at some time uniformly distributed between 5:15 pm and 6:00 pm. Given that Natasha arrives first, what is the probability that she will not have to wait for more than 10 minutes for Sonia? Hint. Let X be the arrival time (in minutes since 5 pm) of Sonia, and Y be the arrival time (in minutes since 5 pm) of Natasha. Note that 0 ≤ X ≤ 60 and 15 ≤ Y ≤ 60. Write the given event and the desired event in terms of X and Y .

Answer 1

as armon prow or let X:- Arrival time of Sonia Let Y - Arrival time of Natasha. Now, According to the required condition Y-X 210 Reg. Probability, ply- X510] - P[Y-102X] Now, since both the arrival times are independent of each other ie X & Y are independent fx,y (x, y) = 1 L 115 sx = 60 45 45 i is sy L 60 - - Foxi 20.01 2 o.1 0.32

2 60 80 wird IP [y-10 Ex- f tit dx dy 15 Y70 2 1 132 [ Toy y s sto (1462.5) - 1 0.7222 45? Probability that to wait for is 0.72282 Natasha will not have more that 10 min,