A circular dartboard of radius 1 foot is at a distance of 20 feet from you. You throw a dart at it and it hits the dartboard at some point Q in the circle. What is the probability that Q is closer to the center of the circle than the periphery?
option
a) 0.75
b) 1
c) 0.5
d) 0.25

• The sample space for this problem have four elements.
  The dart may hit the board 1.Exactly on the circle 2.Closer to circle 3.closer to the periphery 4.Exactly on the periphery.
  
  n(s)=4
  n(dart to hit closer to center)=1
  so probability= 1/4
  
  Ans:0.25
• 14 years agoHelpfull: Yes(72) No(0)
• http://www.mypicx.com/11282010/Dart_Board/
  
  see this picture.
  
  To be Q near to centre than periphery, it shud fall under 1/2 ft radius i.e. the inner circle in the picture.
  
  So Probability = Q's chance of being in inner circle ( rad 1/2 ft) / Q's total chance of being in the dartboard i.e outer circle ( rad 1 ft totally)
  
  = (pi * (1/2)^2)/ (pi * (1)^2)
  
  = (pi/4)/pi
  
  = 1/4
  
  =0.25
• 14 years agoHelpfull: Yes(18) No(2)
• the aresa of circle is pi*r^2
  and fro ques we understand dat radius 0.5
  so we get pi/4
  the area of dartboard is pi*r^2
  pi
  pi/4/pi
  0.25
• 14 years agoHelpfull: Yes(13) No(11)
• Radius is 1 foot.If the point is closer to center it must be within the area of inner circle which has the radius of 1/2 foot.So the probability is =area of inner circle /area of outer circle=(3.14*0.5*0.5)/(3.14*1*1)=0.25
  Therefore Probability is 0.25
• 14 years agoHelpfull: Yes(7) No(3)
• Assume that the point within the circle is chosen at random. Since the radius of the circle is 1 foot hence the point must lie within the inner circle(assumed) having radius 1/2 to be closer to the center then periphery.
  
  And now to calculate probablity just compare the area of both inner and outer circles given as:-
  area of innercircle/ area of outer circle=P*(1/2)^2/P*(1)^2 where p=pi
• 13 years agoHelpfull: Yes(1) No(0)
• Area of cirlce=pi*r*r
  The point to be close to the cirle,its radius should be 1/2of the original radius.
  so, the inner circle perimeter=pi*(r/2)^2
  the ratio 1:4
  therefor , 1/4=0.25
• 14 years agoHelpfull: Yes(0) No(0)
• the answer is 0.25..
• 14 years agoHelpfull: Yes(0) No(4)