What is the probability that your flight will arrive on time

What is the probability that your flight will arrive on time? A point (x, y) is chosen at random in the figure. Q = {(x, y)}: -2

Solution

x^2+y^2 >=1 means (x,y) lies outside the unit circle centred at origin but inside the rectangle

-2<=x<=3 and -2<=y<=0

Rectangle below x axis has length 5 and width 2

Prob for the inequality to be true = 1- (Area of half square /Area of rectangle below x axis)

=1- pi/2 /10 =1- pi/20

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p = 4/25 = 0.16

The events are independent and two outcomes

n =4 and x = 1 or n = 12 and x =3

Hence reqd prob =0.3793*0.1876

= 0.0712