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
ollegr [7]
3 years ago
10

A certain system can experience three different types of defects. Let Ai (i = 1, 2, 3) denote the event that the system has a de

fect of type i. Suppose that
P(A1) = .12 P(A2) = .07 P(A3) = .05

P(A1 U A2) = .13 P(A1 U A3) = .14

P(A2 U A3) = .10 P(A1 ∩ A2 ∩ A3) = .01

a) What is the probability that the system does not have a type 1 defect? (If this is A') then I don't need help on part a

b) What is the probability that the system has both type 1 and type 2 defects?

c) What is the probability that the system has both type 1 and type 2 defects but not a type 3 defect?

d) What is the probability that the system has at most two of these defects?
Mathematics
1 answer:
bulgar [2K]3 years ago
8 0

Answer:

a) 0.88

b) 0.06

c) 0.05

d) 0.99

Step-by-step explanation:

a) Yes you are right, Probability that the system does not have a type 1 defect = P(A1').

It can be calculated using the rule of probability:

   P(A1') = 1 - P(A1)

             = 1 - 0.12

   P(A1') = 0.88

b) The probability that the system has both type 1 and type 2 defects can be calculated by the following formula:

P(A1 ∪ A2) = P(A1) + P(A2)  - P(A1 ∩ A2)

By rearranging the above-mentioned equation, we get:

P(A1 ∩ A2) = P(A1) + P(A2)  - P(A1 U A2)

                   = 0.12 + 0.07 - 0.13

P(A1 ∩ A2) = 0.06

c) Here we need to find the probability that the system has both type 1 and type 2 defects (A1 ∩ A2) but not a type 3 defect which means we need the probability P (A1 ∩ A2 ∩ A3')

For that, we can use the law of probability:

<u>P(A1 ∩ A2) = P(A1 ∩ A2 ∩ A3) + P(A1 ∩ A2 ∩ A3')</u>

By rearranging the above-mentioned equation, we get:

P(A1 ∩ A2 ∩ A3') = P(A1 ∩ A2) - P(A1 ∩ A2 ∩ A3)

                            = 0.06 - 0.01

P(A1 ∩ A2 ∩ A3') = 0.05

d) To find out the probability that the system has at most two of these defects, we will use the probability that all 3 defects are present and subtract it from the total probability (i.e. 1).

<u>P(the system has at most two defects) = 1 - P(the system has all three defects)</u>

We know that the probability of the system having all three defects <u>P(A1 ∩ A2 ∩ A3) = 0.01</u>

So, P(the system has all three defects) = 1 - 0.01

     P(the system has all three defects) = 0.99

You might be interested in
Find the area of the figure. Round your answer to the nearest hundredth, if necessary. (12cm)
Brilliant_brown [7]

Answer:

The answer is 56.52 square centimeters

Step-by-step explanation:

The area of a circle is Pi R^2 so that means the area of a semi circle is half of that which is Pi R^2/2

since diameter is 12, radius = 12/2 = 6

Area = (3.14 × 6^2)÷2 = 56.52

3 0
3 years ago
I will mark brainlyest plss helpp
lana [24]

Answer:

The answer is C

Step-by-step explanation:

i also use khan

5 0
2 years ago
Read 2 more answers
To offset college expenses, at the beginning of your freshman year you obtain a nonsubsidized student loan for $15,000. Interest
soldier1979 [14.2K]

Answer:

15000(1.003425)^12t ;

4.11%

4.188%

Step-by-step explanation:

Given that:

Loan amount = principal = $15000

Interest rate, r = 4.11% = 0.0411

n = number of times compounded per period, monthly = 12 (number of months in a year)

Total amount, F owed, after t years in college ;

F(t) = P(1 + r/n)^nt

F(t) = 15000(1 + 0.0411/12)^12t

F(t) = 15000(1.003425)^12t

2.) The annual percentage rate is the interest rate without compounding = 4.11%

3.)

The APY

APY = (1 + APR/n)^n - 1

APY = (1 + 0.0411/12)^12 - 1

APY = (1.003425)^12 - 1

APY = 1.04188 - 1

APY = 0.04188

APY = 0.04188 * 100% = 4.188%

7 0
3 years ago
Find the height of a parallelogram with an area of 56 and a base of 20.
qaws [65]
The correct answer is 2.8
6 0
3 years ago
What are the points
Goryan [66]

Answer:

There are 9 dots. So 9.

Step-by-step explanation:

Just take my word for it.

7 0
3 years ago
Other questions:
  • Which graph represents the equation x=-2
    7·2 answers
  • Divide $9000 in the Ratio 3:1:6.
    13·1 answer
  • Find an equation of the line with the slope m=6 that passes through the point (4,4). Write the equation in the form Ax + By = C
    6·1 answer
  • Manny used 8 tenth-size parts to model 8/10. Ana used fewer parts to model an equivalent fraction. How does the size of a part i
    5·2 answers
  • To which sets of numbers does π belong?
    13·2 answers
  • Evan washes two types of vehicles. It takes him 30 minutes to wash a car and 40 minutes to wash a truck. He charges $12 to wash
    7·2 answers
  • What is the equation of the parabola shown in the graph
    10·1 answer
  • 2.<br> If 2x - 7 = 19, then x =
    7·1 answer
  • What is the surface area?​
    6·1 answer
  • Two trains leave stations 228 miles apart at the same time and travel toward each other. One train travels at 105 miles per hour
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!