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
If the function rule is to divide by 10, and there is an output value is 7.2, what is the input value?
Sergeeva-Olga [200]
The answer is:  "72" .
______________________________________________
 (input value, or "x")  / 10 = y  = f(x);

When y = 7.2, what is the value of "x" ?


x / 10 = 7.2 ;

x = (7.2) * 10 = 72 .
_______________________
6 0
3 years ago
Kurt opened a savings account and deposited $3,000.00 as principal. The account earns 5%
stiv31 [10]

Answer:

Step-by-step explanation:

P = 3,000

r = 5% = 0.05

t = 9 years

Amount after 9 years is

A = P (1+ r)^t

A = 3,000(1+ 0.05)^9 = 3,000 * 1.05^9 = 4653.984648 ≈ $4,653.98

The balance after 9 years, rounded to the nearest cent is

$4,653 and 98 cents

7 0
2 years ago
Graph the line with a slope of <img src="https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B3%7D" id="TexFormula1" title="\frac{5}{3}" alt
balu736 [363]
I don’t know sorry please somebody else can help you
8 0
2 years ago
Customer: "I see that the amount I owe has been reduced from $90.00 to $75.00." Employee: "Yes, the discount has saved you _____
dusya [7]

Answer:

15 dollers or 22.5%

Step-by-step explanation:

thank you i hope this helps

3 0
3 years ago
Read 2 more answers
Please answer quick! (Number the answers)
Oksana_A [137]

Answer:

All three are yes

Step-by-step explanation:

4. yes

5.yes

6.yes

8 0
3 years ago
Other questions:
  • Nia wants the total weight of her luggage to be no more than 50 kilograms. She has
    12·2 answers
  • Tiffany buys a basket of watermelons on sale for $9 b4 the sales tax ,The sales tax is 9%
    11·1 answer
  • One exterior angle of a regular pentagon has a measure of (2x) what is the value of x
    6·2 answers
  • Helppp it’s due today!!
    7·1 answer
  • y is inversely proportional to the cube of x. It is given that for a certain value of x, the value of y is 7. Find the new value
    14·2 answers
  • The ratio x:y is 3:1
    5·1 answer
  • 15187F0E-816D-4911...F3134C2.jpeg
    7·2 answers
  • Use differences to find a pattern in the sequence.
    10·1 answer
  • And the inverse of f(x) = 3x²-5x+7 <br>​
    8·1 answer
  • Please help me with this question.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!