Latest TCS Aptitude Question SOLUTION: A circular dashboard of radius 1.0 ft is at the distance of 20 ft from you. you throw a dart at it and it hits the dashboard at some point Q in the circle. what is the prob that Q

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A circular dashboard of radius 1.0 ft is at the distance of 20 ft from you. you throw a dart at it and it hits the dashboard at some point Q in the circle. what is the prob that Q is closer to the center of the circle thatn periphery?

Asked In TCS X22 (12 years ago)

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KUMAR VIKASH  (10 years ago)

Forget the 20 feet distance and the 1 ft radius.
Let radius= 2r
As a guide draw a random radius(2r) circle.
Inside it draw a circle of radius r, i.e. of half the radius.
Clearly Q is closer to center if it lies inside the smaller circle.
If E is the event of hitting a point closer to the center,
P(E)= P(hitting inner circle)/P(hitting anywhere in the whole dashboard)
P(E)= Area of inner circle/Area of dashboard
P(E)= pi*r*r/pi*2r*2r = 1/4 or 0.25

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malik suhail taneja  (12 years ago)

if q is closer to the circle..than the perphery then it will lie within the 1,2 feet radius..
so probability =favourable cases/total cases

in this area it s nt the cases it is the are
so area of a circle is directlt propotional to r^2
so p=(1/2)^2 /(1)= 1/4=0.25

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yogesh  (12 years ago)

to hav q clser to cntr dist of q frm cntr shld be < 0.5 ...
so divide d circle into 16 parts each havng 1/16 prob ..
hence der r 4 parts whch r closer to cntr..
so total prob is 4*(1/16)=0.25

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Rimu Mukherjee  (12 years ago)

.25 ll b ans

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