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
Akimi4 [234]
3 years ago
7

In a home theater system, the probability that the video components need repair within 1 year is 0.02, the probability that the

electronic components need repair within 1 year is 0.007, and the probability that the audio components need repair within 1 year is 0.001. Assuming that the events are independent, find the following probabilities. (Round your answers to four decimal places.)
(a) At least one of these components will need repair within 1 year
(b) Exactly one of these component will need repair within 1 year
Mathematics
1 answer:
earnstyle [38]3 years ago
7 0

Answer:

(a) The probability that at least one of these components will need repair within 1 year is 0.0278.

(b) The probability that exactly one of these component will need repair within 1 year is 0.0277.

Step-by-step explanation:

Denote the events as follows:

<em>A</em> = video components need repair within 1 year

<em>B</em> = electronic components need repair within 1 year

<em>C</em> = audio components need repair within 1 year

The information provided is:

P (A) = 0.02

P (B) = 0.007

P (C) = 0.001

The events <em>A</em>, <em>B</em> and <em>C</em> are independent.

(a)

Compute the probability that at least one of these components will need repair within 1 year as follows:

P (At least 1 component needs repair)

= 1 - P (No component needs repair)

=1-P(A^{c}\cap B^{c}\cap C^{c})\\=1-[P(A^{c})\times P(B^{c})\times P(C^{c})]\\=1-[(1-0.02)\times (1-0.007)\times (1-0.001)]\\=1-0.97216686\\=0.02783314\\\approx 0.0278

Thus, the probability that at least one of these components will need repair within 1 year is 0.0278.

(b)

Compute the probability that exactly one of these component will need repair within 1 year as follows:

P (Exactly 1 component needs repair)

= P (A or B or C)

=P(A\cap B^{c}\cap C^{c})+P(A^{c}\cap B\cap C^{c})+P(A^{c}\cap B^{c}\cap C)\\=[0.02\times (1-0.007)\times (1-0.001)]+[(1-0.02)\times 0.007\times (1-0.001)]\\+[(1-0.02)\times (1-0.007)\times 0.001]\\=0.02766642\\\approx 0.0277

Thus, the probability that exactly one of these component will need repair within 1 year is 0.0277.

You might be interested in
PLEASE HELP ME OUT THIS IS DUE TODAY AND I AM STRESSED
spin [16.1K]

Answer:

look up answer key realy would help

Step-by-step explanation:

8 0
3 years ago
Find the first three terms of the sequence below. Tn=n2+2n+9​
klasskru [66]

\\ \bull\tt\longrightarrow T_n=n^2+2n+9

\\ \bull\tt\longrightarrow T_1=1^2+2(1)+9=1+2+9=12

\\ \bull\tt\longrightarrow T_2=2^2+2(2)+9=4+4+9=17

\\ \bull\tt\longrightarrow T_3=3^2+2(3)+9=9+6+9=24

8 0
3 years ago
37 is what percent of 144 to the nearest percent?
Misha Larkins [42]
37 is 26%(rounded up to the nearest percent) of 144
3 0
3 years ago
Simplify completely quantity x squared minus 3 x minus 54 over quantity x squared minus 18 x plus 81 times quantity x squared pl
oee [108]
Your statemtent is incomplete.

I found the samestatment with the complete words: <span>Simplify completely quantity x squared minus 3 x minus 54 over quantity x squared minus 18 x plus 81 times quantity x squared plus 12 x plus </span>36 over x plus 6

Given that your goal is to learn an be able to solve any similar problem, I can teach you assuming that what I found is exactly what you need.

x^2 - 3x - 54            x^2 + 12x + 36
------------------    x   ---------------------
x^2 - 18x + 81              x + 6

factor x^2 - 3x - 54 => (x - 9)(x + 6)

factor x^2 - 18x + 81 => (x - 9)^2

factor x^2 + 12x + 36 = (x + 6)^2

Now replace the polynomials with the factors=>

(x - 9) (x + 6) (x + 6)^2        (x + 6)^2       x^2 + 12x + 36
------------------------------ =  --------------- = --------------------
    (x - 9)^2 (x + 6)                 (x - 9)               x - 9

4 0
3 years ago
Read 2 more answers
Raja drew a circle and labeled the center S. He used the expression 12. to find the
Aleonysh [2.5K]

Answer:a

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • A shoe repairman is working with his assistant, who takes 1.5 times as long to repair a pair of shoes. Together they can fix 20
    6·2 answers
  • The right triangle shown has angles x, y, and z and side lengths a, b, and
    5·1 answer
  • Can a zero slope be a function
    6·2 answers
  • Kira is a software saleswoman. Her base salary is $1600 , and she makes an additional $80 for every copy of History is Fun she s
    15·1 answer
  • Yo help me with number 6 pls thx and tell me how. I can't find the answer
    7·1 answer
  • The volume of a right circular cone increased by a factor of 25. If the height remained fixed, by what factor was the radius cha
    6·1 answer
  • Tool bella bought 10 copies of jakes first CD at 14.56 cents per copy. how much did she spend
    12·1 answer
  • 9
    8·1 answer
  • HELP ME OUT HERE PLEASEEEEE
    6·2 answers
  • Help me with this question.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!