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
victus00 [196]
3 years ago
14

Motor vehicles sold to individuals are classified as either cars or light trucks (including SUVs) and as either domestic or impo

rted. In a recent year, 69% of vehicles sold were light trucks, 78% were domestic, and 55% were domestic light trucks.
Let A be the event that a vehicle is a car and B the event that it's imported. Write each of the following events in set notation and give its probability.
(a) The vehicle is a light truck.
(b) The vehicle is an imported car.
Mathematics
1 answer:
Rudik [331]3 years ago
4 0

Answer:

a) Probability that vehicle is Light Truck is 0.69

b) Probability that vehicle is imported car is 0.08 or 8%.

Step-by-step explanation:

Part a)

Event that vehicle is a car is given by A. Since, the vehicles can only be classified as cars or light trucks, the event that a vehicle will be light truck will be compliment of A.

i.e. Event that vehicle is a Light Truck = A^{c}

It is given that in recent year 69% of vehicles sold were light trucks, 78% were domestic, and 55% were domestic light trucks.

So, from here we can say that, if a vehicle is randomly selected from all the vehicles the probability that it would be a light truck will be:

P(Vehicle will be Light Truck) = P(A^{c}) = 69% = 0.69

Part b)

Event that vehicle is imported is given by B. We need to find the probability the a randomly chosen vehicle is an imported car i.e. we have to find probability of occurrence of events A and B together, which will be denoted as: P(A and B)

Since, P(A^{c}) = 69% = 0.69

P(A) = 1 - P(A^{c}) = 1 - 0.69 = 0.31

It is also given that 78% of vehicles were domestic. This means, the percentage/probability of imported vehicles is:

P(B) = 1 - 0.78 = 0.22

55% of vehicles were domestic light trucks. This can be expressed as:

P(A^{c}\&B^{c}), the compliment of this event will give us P(A or B).

i.e.

P(A or B) = 1 - P(A^{c} \&B^{c}) = 1 - 0.55 = 0.45

According to the addition rule of probabilities:

P(A or B) = P(A) + P(B) - P(A and B)

Substituting the calculated values gives us:

0.45 = 0.31 + 0.22 - P(A and B)

P(A and B) = 0.08

This means, the probability that vehicle is imported car is 0.08 or 8%.

You might be interested in
The sum of the measures of the external angles of any polygon is
Leona [35]

Answer:

The sum of all the exterior angles in a polygon is equal to 360 degrees.

Hope this helps you. Do mark me as brainliest.

3 0
3 years ago
Been here for hours please help me
mezya [45]

Answer:

free points

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Suppose the function y = 30,000(1.06)x models the annual profit for a small business x years after 2000. Find the profit at the
goldfiish [28.3K]
From 2000 to 2011, there are 11 years. From the given function, we can calculate the profit for a small business at the end of 2011 by substituting 11 to the x of the given equation. 
                                         y = (30,000)(1.06)(11)
                                         y = 349,800
Thus, the profit at the end of 2011 is approximately $349,800. 
4 0
3 years ago
Leanne runs on the treadmill and rides the exercise bike at the gym to stay in shape. She burns 15 calories per minute on the tr
sergiy2304 [10]

Answer: C.

Explanation: i just took it. and got a 100. :)

8 0
2 years ago
if 62% percent of people voted in a community of about 55,200 eligible voters how many people were registerd
solniwko [45]
62% of 55,200...turn ur percent to a decimal..." of " means multiply
0.62(55,200) = 34,224 <==

although, just because u r registered, does not mean u vote.
6 0
3 years ago
Other questions:
  • Given b(x) = X+41, what is b(-10)?
    11·1 answer
  • Study the triangle. What can you conclude about the angle measures? The angle measures are 30°, 60°, and 90°. The angle measures
    5·2 answers
  • If I round the number 43,257,529 to 43,300,000 what place value did I round the number to
    15·1 answer
  • The total amounts of rainfall at various points in time during a thunderstorm are shown in the table. Rainfall During a Thunders
    8·2 answers
  • 1. In diagram below, POTU is a circle and |SR|=|ST|. Find.r.<br>​
    5·2 answers
  • the volume of a large sphere (of radius R) is twice the volume of a smaller sphere (of radius r). form an equation linking r and
    8·1 answer
  • Help MEEEEEE PLEASEEEEEEE
    14·2 answers
  • Celik, S. (2011). A media comparison study on first aid instruction. Health Education Journal. 72(1), 95-101
    7·1 answer
  • Determine the range of the following graph
    8·1 answer
  • Which one does 3 equal :) <br> Please let me know and why
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!