Mathematics: Help me solve this explain steps too

The probability of that you will have salt packed with your dinner is Further explanation: The probability can be obtained as the ratio of favorable number of outcomes to the total number of outcomes. Given: John packs of the dinners, Mary packs of the dinners and Sue packs the remaining dinners. Of the dinners John packs do not include a salt packet. If Mary packs the dinner of the time the salt is omitted. Lastly, of the dinners do not include salt if Sue does the packing. Explanation: The probability...

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Ответ:

1hannacarson

06.11.2020

Mathematics

The probability of that you will have salt packed with your dinner is $\boxed{0.968}.$

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,

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

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 you will have salt packed with your dinner can be expressed as follows,

$\begin{aligned}{\text{Probability}}\left( {{\text{salt}}} \right) &= 1 - {\text{Probability}}\left( {{\text{No salt}}} \right)\\&= 1 - \left( {0.45 \times 0.04 + 0.25 \times 0.02 + 0.30 \times 0.03} \right)\\&= 1 - 0.032\\&= 0.968\\\end{aligned}$

The probability of that you will have salt packed with your dinner is $\boxed{0.968}.$

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.

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