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 %
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
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%
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%
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
https://web2.0calc.com/img/upload/9dc0601484f88e63c19f0354/ugh3.jpg
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