#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 = [ ( 9^{2} ) - ( pi(9/2)^{2} ) ] / [ 9^{2} ]

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

probability = 1 - pi/4

probability ≈ 0.215

probability ≈ 21.5 / 100

probability ≈ 21.5 %

hectictar 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

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%

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%

CPhill 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

CPhill Oct 23, 2018

#6**+1 **

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

hectictar Oct 23, 2018