Probability that a randomly selected point within the circle falls in the white area will be [tex]0.67[/tex] .
What is Probability ?
Probability is the ratio of the number of outcomes to the total number of possible outcomes.
Probability [tex]=\frac{Number\ of\ possible\ outcomes}{Total\ number\ outcomes}[/tex]
We have,
Radius [tex]=4[/tex] cm
Now,
Area of Circle [tex]=\pi r^{2}[/tex]
Area of Circle[tex]=\frac{22}{7} *4^2=50.28\ cm^2[/tex]
Now,
Area of minor segment [tex]=\frac{\theta}{360^0} *\pi r^{2}[/tex]
Area of minor segment [tex]=\frac{60}{360} *\frac{22}{7}* 4^{2}=8.38\ cm^2[/tex]
Now,
We have two minor segment,
Area of two minor segment [tex]=8.38*2=16.76\ cm^2[/tex]
Now,
Area of white Portion [tex]=50.28-16.76=33.52\ cm^2[/tex]
Now,
Probability [tex]=\frac{Number\ of\ possible\ outcomes}{Total\ number\ outcomes}[/tex]
Probability [tex]=\frac{33.52}{50.28}=0.67[/tex]
So, the Probability of white area is [tex]0.67[/tex] .
Hence, we can say that Probability that a randomly selected point within the circle falls in the white area will be [tex]0.67[/tex] .
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