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The table below represents the data collected at a sandwich shop for the last six months with respect to the type of bread people ordered (sourdough or wheat) and whether or not they got cheese on their sandwich.

What is the P(cheese | wheat) ? Show all work to receive full credit.

The table below represents the data collected at a sandwich shop for the last six-example-1
User Oravecz
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2 Answers

2 votes

Answer:

The number of times people got cheese and wheat is 1200

Explanation:

Hope this helps! Have a good day! :)

User Licysca
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9 votes

Answer:


\sf (12)/(19)

Explanation:

To begin, add the column and row totals to the table (see attachment).

Let W = Wheat

Let C = With cheese


\sf Probability\:of\:an\:event\:occurring = (Number\:of\:ways\:it\:can\:occur)/(Total\:number\:of\:possible\:outcomes)


\implies \sf P(W)=(1900)/(3125)=(76)/(125)


\implies \sf P(C)=(2000)/(3125)=(16)/(25)


\implies \sf P(W \cap C)=(1200)/(3125)=(48)/(125)

As the events W and C are not independent, we can use the formula:


\sf P(C\: | \:W)=(P(W \cap C))/(P(W))

Substituting the values into the formula:


\sf P(C\: | \:W)=((48)/(125))/((76)/(125))=(48)/(76)=(12)/(19)

The table below represents the data collected at a sandwich shop for the last six-example-1
User Rimma
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