Mathematics, 07.10.2019 14:30 madi2878

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

Answers: 3

Show answers

Answers

Answer from: anonymousanon

The probability that Mary packed the dinner is 0.15625

Further explanation

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 :

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

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

$Probability = \frac{0.005}{0.032}$

$\large {\boxed {Probability = 0.15625} }$

Learn moreDifferent Birthdays : Dependent or Independent Events : Mutually exclusive : Answer details

Grade: High School

Subject: Mathematics

Chapter: Probability

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

Three workers at a fast food restaurant pack the take-out chicken dinners. john packs 45% of the din

Answer from: jade11710

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://.

2. Learn more about equation of circle .

3. Learn more about range and domain of the function .

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.

Answer from: Quest

answer: 12

step-by-step explanation:

Answer from: Quest

if you are saying purchasing 3 social media ads and one newspaper ad counts as one purchase then there are:

6 purchases

if you are asking how many of each then:

18 social media ads

6 newspaper ads

Another question on Mathematics

Mathematics, 21.06.2019 18:00

Liz is shipping a package to her friend.the maximum weight of a medium flat-rate box is 20 pounds,including the box which weighs 6 ounces.write and solve an inequality to describe the possible weight ,w, of the contents that liz will ship to her friend if she must use a medium flat-rate box.

Answers: 2

Answer

Mathematics, 21.06.2019 18:10

What is the ratio for the surface areas of the cones shown below, given that they are similar and that the ratio of their radil and altitudes is 4: 3? 23

Answers: 1

Answer

Mathematics, 21.06.2019 19:40

What is the range of the function? f(x)=-2|x+1|? a. all real numbers. b. all real numbers less than or equal to 0. c. all real numbers less than or equal to 1. d. all real numbers greater than or equal to 1

Answers: 2

Answer

Mathematics, 21.06.2019 21:00

Isabel graphed the following system of equations. 2x – y = 6 y = -3x + 4 she came up with the solution (2,-2). what were the 3 steps she did to get that solution? (make sure they are in the correct order)

Answers: 2

Answer

You know the right answer?

Three workers at a fast food restaurant pack the take-out chicken dinners. john packs 45% of the din...

Questions