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
Kisachek [45]
3 years ago
15

Three workers at a fast food restaurant pack the take-out chicken dinners. John packs 45% of the dinners, Mary packs 25% of the

dinners and Sue packs the remaining dinners. Of the dinners John packs 4% do not include a salt packet. If Mary packs the dinner 2% of the time the salt is omitted. Lastly, 3% of the dinners do not include salt if Sue does the packing. If you find there is not salt in your purchased dinner what is the probability that Mary packed your dinner? 0.5625 0.018 0.032 0.15625 0.005

Mathematics
2 answers:
Gekata [30.6K]3 years ago
8 0

The probability that Mary packed the dinner is 0.15625

<h3>Further explanation</h3>

The probability of an event is defined as the possibility of an event occurring against sample space.

Let us tackle the problem.

This problem is about Conditional Probability.

in general, the formula we will use is as follows :

\large {\boxed {P ( A | B ) = P ( A \bigcap B ) \div P ( B )} }

Let:

The probability of John that packs the dinners without salt packet is P(J)

The probability of Mary that packs the dinners without salt packet is P(M)

The probability of Sue that packs the dinners without salt packet is P(S)

Then :

P(J) = 45\% \times 4\% = 0.018

P(M) = 25\% \times 2\% = 0.005

P(S) = 30\% \times 3\% = 0.009

If I find there is not salt in my purchased dinner, then the probability that Mary packed my dinner is :

Probability = \frac{P(M)}{P(J) + P(M) + P(S)}

Probability = \frac{0.005}{0.018 + 0.005 + 0.009}

Probability = \frac{0.005}{0.032}

\large {\boxed {Probability = 0.15625} }

<h3>Learn more</h3>
  • Different Birthdays : brainly.com/question/7567074
  • Dependent or Independent Events : brainly.com/question/12029535
  • Mutually exclusive : brainly.com/question/3464581

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Sample , Space , Six , Dice , Die , Workers , Fast Food Restaurant , Salt Packet , Dinner

FinnZ [79.3K]3 years ago
6 0

The probability of that Mary packed for dinner and the dinner contains no salt is \boxed{0.15625}.

Further explanation:

The probability can be obtained as the ratio of favorable number of outcomes to the total number of outcomes.

\boxed{{\text{Probability}} = \frac{{{\text{Favorable number of outcome}}}}{{{\text{Total number of outcomes}}}}}

Given:

John packs 45\% of the dinners, Mary packs 25\% of the dinners and Sue packs the remaining dinners. Of the dinners John packs 4\% do not include a salt packet. If Mary packs the dinner 2\% of the time the salt is omitted. Lastly,3\% of the dinners do not include salt if Sue does the packing.

Explanation:

The probability of John packs the dinner can be expressed as follows,

\begin{aligned}{\text{Probability}}\left( {{\text{John}}} \right)&= 45\%\\&= 0.45\\\end{aligned}

The probability of Mary packs the dinner can be expressed as follows,

\begin{aligned}{\text{Probability}}\left( {{\text{Mary}}} \right) &= 25\% \\&= 0.25\\\end{aligned}

The probability of Sue packs the dinner can be expressed as follows,

\begin{aligned}{\text{Probability}}\left( {{\text{Sue}}} \right) &= 1 - 0.45 - 25\\&= 1 - 0.70\\&= 0.30\\\end{aligned}

The probability of no salt packet is packed given that the John packs for dinner can be expressed as follows,

P\left( {\dfrac{{{\text{No salt}}}}{{{\text{John packs}}}}} \right) = 0.04

The probability of no salt packet is packed given that the Mary packs for dinner can be expressed as follows,

P\left( {\dfrac{{{\text{No salt}}}}{{{\text{Mary packs}}}}} \right) = 0.02

The probability of no salt packet is packed given that the Sue packs for dinner can be expressed as follows,

P\left( {\dfrac{{{\text{No salt}}}}{{{\text{Sue packs}}}}} \right) = 0.03

The probability of that Mary packed for dinner and the dinner contains no salt can be expressed as follows,

{\text{P}}\left( {\dfrac{{{\text{Mary purchased}}}}{{{\text{No salt}}}}} \right) = \frac{{P\left( {{\text{Mary}}} \right) \times P\left( {\dfrac{{{\text{No salt}}}}{{{\text{Mary}}}}} \right)}}{{P\left( {{\text{John}}} \right) \times P\left( {\dfrac{{{\text{No salt}}}}{{{\text{John}}}}} \right) + P\left( {{\text{Mary}}} \right) \times P\left( {\dfrac{{{\text{No salt}}}}{{{\text{Mary}}}}} \right) + P\left( {{\text{Sue}}} \right) \times P\left( {\dfrac{{{\text{No salt}}}}{{{\text{Sue}}}}} \right)}}

The probability can be obtained as follows,

\begin{aligned}{\text{P}}\left( {\frac{{{\text{Mary purchased}}}}{{{\text{No salt}}}}} \right) &= \frac{{0.25 \times 0.02}}{{0.45 \times 0.04 + 0.25 \times 0.02 + 0.30 \times 0.03}}\\&= \frac{{0.005}}{{0.018 + 0.005 + 0.009}}\\&= \frac{{0.005}}{{0.032}}\\&= 0.015625\\\end{aligned}

The probability of that Mary packed for dinner and the dinner contains no salt is \boxed{0.15625}.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497.

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Three worker, fast food, restaurant pack, chicken dinners, John packs, 45% of the dinners, Mary, 25% of dinner, Sue packs remaining, 4% so not include salt, salt packet, salt is omitted, dinner, 2%, 3%, purchased dinner, probability, 0.5625, 0.018, 0.032, 0.15625, 0.005.

You might be interested in
How to solve this one​
ladessa [460]

A dotted line is not included in the solution so there is no equal sign.

The blue area is to the right of the dotted line so the solution is >

The line crosses the x axis at -2

The answer is : x-y > -2

4 0
3 years ago
What is the answer to <br>11-9m=-70
Fynjy0 [20]

Answer:

m=9

Step-by-step explanation:

11-9m=-70

-11        -11

-9m  =  -81

divide both sides by -9 and you get m=9

7 0
3 years ago
Read 2 more answers
Use simultaneous equations to solve the following. Three kilograms of jam and two kilograms of butter cost $29 and six kilograms
artcher [175]

Answer:

The cost of 1kg jam is $7 and the cost of 1kg butter is $4

Step-by-step explanation:

Let jam = x

butter = y

3x + 2y = 29 -----(1)

6x + 3y = 54 -----(2)

(1)×2 ->

6x + 4y = 58 -----(3)

(3)-(2) ->

y = 4

suby=4into(2)

6x + 3(4) = 54

6x = 42

x = 7

(Correct me if i am wrong)

6 0
3 years ago
PLEASE HELP!!<br> How many solutions can be found for the equation −4x − 11 = 2(x − 3x) + 13?
PilotLPTM [1.2K]

Answer: No~Solutions

Step-by-step explanation:

Let's factor then solve to find the complex solutions.

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : -4x-11=2(x-3x)+13

Equations that are never true:

1.1     ~~~~ Solve :    -24   =  0

This equation has no solution.

A non-zero constant never equals zero.

<u><em>Therefore your answer is </em></u>No~Solution

3 0
2 years ago
Please help as soon as possible
GenaCL600 [577]

Answer:

The first is -4 and the second is 10

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Why should you avoid investing all your money in familiar stocks
    12·1 answer
  • What percent of the June budget was for Tim's Chevron and car (to the nearest tenth)?
    11·1 answer
  • I understand this.....
    8·2 answers
  • HELP PLEASE I NEED TO KNOW --&gt; SUPER EASY QUESTION
    11·1 answer
  • Ralph has sliced a pizza using straight line cuts through the center of the pizza. the slices are not exactly the same size. Ral
    14·2 answers
  • Perform the operation,<br> (-2x^2 – 2x + 1) +(-8x^2-7)
    12·1 answer
  • Roddy runs a 7-day, 10,000-person simulation several times, and finds that nobody has won the contest in any of his simulations.
    5·1 answer
  • WILL MARK BRAINLIEST PLS HELP ITS DUE
    7·2 answers
  • Can someone plz help me with this one problem
    12·2 answers
  • 20/28 in its simplest form what is it ?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!