A project conducted by the Australian Federal Office of Road Safety asked people many questions about
their cars. One question was the reason that a
... [Show More] person chooses a given car, and that data is in table
#4.1.4 ("Car preferences," 2013).
Table #4.1.4: Reason for Choosing a Car
Safety Reliability Cost Performance Comfort Looks
84 62 46 34 47 27
Find the probability a person chooses a car for each of the given reasons.
Solution:
Safety: 84/300 = 28%
Reliability: 62/300 = 21%
Cost: 46/300 = 15%
Performance: 34/300 = 11%
Comfort: 47/300 = 15%
Looks: 27/300 = 9%
4.2.2
Eyeglassomatic manufactures eyeglasses for different retailers. They test to see how many defective
lenses they made in a time period. Table #4.2.2 gives the defect and the number of defects.
Table #4.2.2: Number of Defective Lenses
Defect type Number of defects
Scratch 5865
Right shaped – small 4613
Flaked 1992
Wrong axis 1838
Chamfer wrong 1596
Crazing, cracks 1546
Wrong shape 1485
Wrong PD 1398
Spots and bubbles 1371
Wrong height 1130
Right shape – big 1105
Lost in lab 976
Spots/bubble – intern 976
a.) Find the probability of picking a lens that is scratched or flaked.
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b.) Find the probability of picking a lens that is the wrong PD or was lost in lab.
c.) Find the probability of picking a lens that is not scratched.
d.) Find the probability of picking a lens that is not the wrong shape.
a) Scratched: 5865/25891 = 22%
Flaked: 1992/25891 = 7%
b) Wrong PD: 1398/25891 = 5%
Lost in lab: 976/25891 = 37%
c) Not scratched: Right shaped (big) + Right shaped (small)/25891
5708/25891 = 22%
d) Wrong shape: 1485/25891 = 5%
4.2.8
In the game of roulette, there is a wheel with spaces marked 0 through 36 and a space marked 00.
a.) Find the probability of winning if you pick the number 7 and it comes up on the wheel.
Probability: 1/38
b.) Find the odds against winning if you pick the number 7.
Solution: 1-1/38
37/38
c.) The casino will pay you $20 for every dollar you bet if your number comes up. How much
profit is the casino making on the bet?
The Expected gain is 1/38 *20 = $0.58
37/38 - 19*1/38 = = 0.474
Profit casino is making on the bet = $0.474
4.4.6 Find
10P6
Npr = n!/(n-r)!
10p6 = 10!/(10-6)!
Numerator n!:
N! = 10!
10! = 10*9*8*7*6*5*4*3*2*1
10! = 3,628,800
Denominator:
(n-r)! = (10-6)!
(10-6)! = 4!
4!=4*3*2*1 [Show Less]