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
Ahat [919]
2 years ago
7

Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The results from 100 sam

ples are summarized as follows:
conforms
yes no
1 22 8
supplier 2 25 5
3 30 10

Let A denote the event that a sample is from supplier 1, and let B denote the event that a sample from any supplier conforms to specifications. If a disk is selected at random, determine the following probabilities.

a. P(A)=0.3
b. P(B)=0.77
c. P(A ∩ B) =0.22
d. P(A U B)=0.85
Mathematics
1 answer:
Vlad [161]2 years ago
7 0

Answer

P(A) = 0.30

P(B) = 0.77

P(A\ n\ B) = 0.22

P(A\ u\ B) = 0.85

Explanation:

Given

See attachment for proper data presentation

n = 100 --- Sample

A = Supplier 1

B = Conforms to specification

Solving (a): P(A)

Here, we only consider data in sample 1 row.

Here:

Yes = 22 and No = 8

n(A) = Yes + No

n(A) = 22 + 8

n(A) = 30

P(A) is then calculated as:

P(A) = \frac{n(A)}{Sample}

P(A) = \frac{30}{100}

P(A) = 0.30

Solving (b): P(B)

We only consider data in the Yes column.

Here:

(1) = 22    (2) = 25 and (3) = 30

n(B) = (1) + (2) + (3)

n(B) = 22 + 25 + 30

n(B) = 77

P(B) is then calculated as:

P(B) = \frac{n(B)}{Sample}

P(B) = \frac{77}{100}

P(B) = 0.77

Solving (c): P(A n B)

Here, we only consider the similar cell in the yes column and sample 1 row.

i.e. [Supplier 1][Yes]

This is represented as: n(A n B)

n(A\ n\ B) = 22

The probability is then calculated as:

P(A\ n\ B) = \frac{n(A\ n\ B)}{Sample}

P(A\ n\ B) = \frac{22}{100}

P(A\ n\ B) = 0.22

Solving (d): P(A u B)

This is calculated as:

P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)

This gives:

P(A\ u\ B) = \frac{30}{100} + \frac{77}{100} - \frac{22}{100}

Take LCM

P(A\ u\ B) = \frac{30+77-22}{100}

P(A\ u\ B) = \frac{85}{100}

P(A\ u\ B) = 0.85

You might be interested in
Shirts are onsale at 3 for $15.50. how many shirts can you buy with $139.50.
Goshia [24]
If one shirt is sold for $15.50, the amount of shirts you'd be able to buy with $139.50 is 9.

Multiply 9 by 3 and you get your answer: 27 Shirts
5 0
3 years ago
Read 2 more answers
The grocery store sells bacon for $5.30 per pound.<br> Write a function to represent the situation.
aliina [53]

Answer:

5.30x p

Step-by-step explanation:

(p stands for how many pounds are bought

3 0
2 years ago
Scale factor of 3 and 6
GenaCL600 [577]

Answer:

3:6

3x2=6

Scale factor = 2

Step-by-step explanation:

3 0
3 years ago
19. A quadratic equation is shown below.
victus00 [196]

Answer:

\{\sqrt b, -\sqrt b\}

Step-by-step explanation:

Given

a^2 - b = 0

Required

Determine the solution

Since b is  a perfect square, the equation can be expressed as:

a^2 - (\sqrt b)^2 = 0

Apply difference of two squares:

(a - \sqrt b)(a + \sqrt b) = 0

Split:

(a - \sqrt b)= 0 \ or\ (a + \sqrt b) = 0

Remove brackets:

a - \sqrt b= 0 \ or\ a + \sqrt b = 0

Make a the subject in both equations

a =\sqrt b \ or\ a  =-\sqrt b

The solution can be represented as:

\{\sqrt b, -\sqrt b\}

6 0
2 years ago
I NEED HELPPPP PLEASE RN!!
Romashka-Z-Leto [24]

Answer:

is A

Step-by-step explanation

b you n t p

3 0
3 years ago
Read 2 more answers
Other questions:
  • 4x-5=2(2x+1) find the x
    6·2 answers
  • Conner bought a birthday card for $2.19,gift wrap for $3.89,and a game for $13.13. Estimate the total cost
    10·1 answer
  • a rectangle has length 3 cm greater than its width.it has an area of 28cm squared,find the dimensions of the rectangle
    13·1 answer
  • What is x <br> x - 3 = -5
    15·2 answers
  • EMERGENCY! DUE VERY SOON! HELP!
    12·1 answer
  • Find the perimeter and area of a rectangle with a length of 3.2m and a width of 1.5m
    5·2 answers
  • Consider the quadratic function f(x) = 2x2 – 8x – 10. The x-component of the vertex is . The y-component of the vertex is . The
    14·2 answers
  • Please show me How to do this number
    8·1 answer
  • Given the diameter of a circle is 17 1/2cm, find its area (use π = 22/7)​
    8·1 answer
  • There are 15 coins, which are nickels and dimes only, in Ediths purse. The total value of the coins in her purse is $1.15. If n=
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!