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PLEASE HELP

Find the probability that a randomly
selected point within the circle falls
in the white area.
60°
60°
r = 4 cm
[? ]%
Round to the nearest tenth of a percent.

PLEASE HELP Find The Probability That A Randomly Selected Point Within The Circle Falls In The White Area 60 60 R 4 Cm Round To The Nearest Tenth Of A Percent class=

Sagot :

hekmatawalkhil

Answer:

probability is 0.67

Step-by-step explanation:

We know that Angle in a circle = 360°

Area of total shaded parts = 60 + 60 = 120°

Area of total unshaded parts = 360-120 = 240°

Probability that a random selected point within the circle falls in the unshaded area

= 240/360

= 2/3= 0.67

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] .

To know more about Probability click here

https://brainly.com/question/27579447

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