1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
SIZIF [17.4K]
3 years ago
12

Seventy percent of all vehicles examined at a certain emissions inspection station pass the inspection. Assuming that successive

vehicles pass or fail independently of one another, calculate the following probabilities
(a) P(all of the next three vehicles inspected pass)
(b) P(at least one of the next three inspected fails
(c) P(exactly one of the next three inspected pass)
(d) P(at most one of the next three vehicles inspected passes)
(e) Given that at least one of the next three vehicles passes inspection, what is the probability that all three pass (a conditional probability)?
Mathematics
1 answer:
miss Akunina [59]3 years ago
7 0

Answer:

a. 0.343

b. 0.657

c. 0.189

d. 0.216

e. 0.353

Step-by-step explanation:

We use the combination formula of probability distribution to solve the question.

Where P(x=r) = nCr * p^r * q^n-r

Where n = number of trials = 3 vehicles

r = desired outcome of trial which varies.

p = probability of success = 70% =0.7

q = probability of failure = 1-p = 0.3

a. Probability that all 3 vehicles passed = P(X=3)

= 3C3 * 0.7^3 * 0.3^0 = 1 * 0.343 * 1

= 0.343.

b. Probability that at least one fails = 1 - (probability that none failed)

And probability that none failed = probability that all 3 vehicles passed.

Hence Probability that at least one fails = 1 - (probability that all 3 vehicles passe)

= 1 - 0.343

= 0.657

c.) probability that exactly one pass= P(X=1)

= 3C1 * 0.7¹ * 0.3² = 3 * 0.7 * 0.09

= 0.189

d.) probability that at most One of the vehicles passed = probability that none passed + probability of one passed.

Probability that none of the vehicles passed = P(X=0)

= 3C0 * 0.7^0 * 0.3^3 = 1*1*0.027

=0.027

Probability that one passed as calculated earlier = 0.189

Hence probability that at most one vehicle passed = 0.189 + 0.027 = 0.216

e.) Probability that all three Vehicles pass given that at least one pass = (probability of all three vehicles passes) / (probability that at least one passes)

Probability that at least one pass = 1 - probability that none passed.

= 1 - 0.027

= 0.973

Hence,

Probability that all three Vehicles passed given that at least one passed = 0.343/0.973

= 0.3525 = 0.353 (3.d.p)

You might be interested in
Explain how to write an equival3nt expresion using the associative property<br><br> 2+(11+y)​
nignag [31]

Answer:

13 + y

Step-by-step explanation:

hope i helped :) !

brainliest pleaseee !!?

3 0
3 years ago
The temperature of a hot steak starts at 140f and decreases at 5f per minute what will the temperature of this steak after a cer
irina1246 [14]

Answer:

T(m) = (140 - 5m)

Step-by-step explanation:

Given that :

Initial temperature, a = 140 F

Rate of decrease = 5 F per minute

Given a certain Number of minutes, m

Temperature, T after m minutes ;

Using the formula :

Final temperature = Initial temperature - 5*number of minutes)

T(m) = (140 - 5m)

Given that ; m = 10

T(10) = 140 - 5(10)

T(10) = 140 - 50

T(10) = 90 F

7 0
3 years ago
Find the exact values of the six trigonometric functions of the angle shown in the figure.
lana66690 [7]

Answer:

X

G

D

D

D

E

E

E

EW

G

H

F

I

U

TD

SQ

U

W

4

FW

S

W

WS

W

3 0
2 years ago
In the xy-plane, the equations x + 2 = 10 y and 3 +6 = x y c represent the same line for some constant c. What is the value of c
aalyn [17]

Answer:

C=30

Step-by-step explanation:

Supposing that we have the lines

x+2=10y

and

3x+6=Yc.

Note that dividing by 3 the second line can be rewritten as

x + 2= Y c/3.  

Remember that a line is written as ax+b=dY, in our case, both lines have a=1 and b=2. Therefore, in orther that the two lines are equal, we need that 10=c/3, hence c=30.

3 0
3 years ago
Which number is a factor of 12 but not a multiple of 3?
Delvig [45]
First list all the factors of 12;

1, 2, 3, 4, 6, 12

now let's see which ones are multiples of 3;

3, 6, 12 

so all we have left are numbers 1, 2 and 4.

hope that helps, God bless!
6 0
3 years ago
Other questions:
  • Please answer this correctly without making mistakes
    10·1 answer
  • How does -1/3 relate to 3
    9·1 answer
  • A pharmacist needs 100 gallons of 50% alcohol solution. She has available a 30% solution and an 80% solution. How much of each s
    12·2 answers
  • A cone has a diameter of 7 cm and a slant height of 15.5 cm. What is the surface area of the cone?
    13·2 answers
  • How to expend 5(3z+b) +4(b-2z) using distributive property​
    6·2 answers
  • The price of cable TV has risen over the past 20 years.
    8·2 answers
  • PLEASE BE RIGHT AND SOLVE
    9·2 answers
  • I need super help with this one.
    9·1 answer
  • Find an equation of the straight line that is perpendicular to the straight line x+2y=5 and that passes through the point (3,7)
    8·1 answer
  • What is a line that intersects a circle at exactly one point? *
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!