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# Help

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6    Oct 23, 2018

#1
+2

A circle is inscribed in a square with a side length of 9. What is the probability that a randomly chosen point lies in the square, but not in the circle? Express your answer as a percent rounded to the nearest tenth.

probability  =  target area / total area

probability  =  [area of square - area of circle] / [area of square]

probability  =  [ ( 92 )  -  ( pi(9/2)2 ) ] / [ 92 ]

probability  =  [ 81 - pi(81/4) ] / 81

probability  =  1 - pi/4

probability  ≈  0.215

probability  ≈  21.5 / 100

probability  ≈  21.5 %

Oct 23, 2018
#2
+1

First one

The length of the square's side doesn't matter.....the probability is independent of this

The radius of the circle  = r

The side of the square  = 2r

The area of the circle =   pi * r^2    (1)

The area of the square  =  (side)^2  = ( 2r)^2  = 4r^2   (2)

So....the area  betweem the area of the square and the area of the circle  = (2) - (1)  =

4r^2  - pi r^2   =    r^2 [ 4 - pi ]

So....this area to the total area of the square is the probability  =

r^2  [ 4 - pi ]               4 - pi

___________  =      ______     ≈  .2146   ≈  21.5%

4r^2                          4   Oct 23, 2018
edited by CPhill  Oct 23, 2018
#3
+1

Second one

First part

P (  on first cube and 2 on second cube)  =   1/6  *  1/6 =  1/36

Second part

We have 11 cars and 3 are red

Peter  has  3/11 chance of getting a red one

Assuming that Peter gets a red one. there are 2 red cars left out of 10

So...the probability that Richard gets  a red one is  2/10  = 1/5

So

P ( A and B)   =   3/11  *  1/5   =    3 / 55  ≈  .0545  ≈    5.5%   Oct 23, 2018
edited by CPhill  Oct 23, 2018
#4
+1

Third  one

P ( previous work experience  and rated satisfactory )

The probability is just the product of the percentages along the apprpriate tree branches =

.75 * .85   =    .6375   =  63.75 %  ≈  64%   Oct 23, 2018
#5
+1

We have   12 + 5 + 9   =  26  people who liked the movie

The number in the 18-34 group   is 12

So....the probability  od 18-34   given that a person liked the movie is :

12 / 26   =     6 / 13  ≈   .46   Oct 23, 2018
#6
+1

Pretend that we just got all the people that liked the movie in a room together. The question is what is the probability that a randomly selected person in that room is aged 18-34 ?

probability  =  number of people aged 18-34 in the room / number of people in the room

probability  =  num of people aged 18-34 that liked the movie / num of people that liked the movie

probability  =  12 / (12 + 5 + 9)

probability  =  12 / 26

probability  ≈  0.46

Oct 23, 2018