In an effort to find the source of an outbreak of food poisoning at a conference, a team of medical detectives carried out a study. They examined all $50$people who had food poisoning and a random sample of $200$people attending the conference who didn’t get food poisoning. The detectives found that $40\%$of the people with food poisoning went to a cocktail party on the second night of the conference, while only $10\%$of the people in the random sample attended the same party. Which of the following statements is appropriate for describing the $40\%$of people who went to the party? (Let F = got food poisoning and A = attended party.)

(a) P(F | A) = 0.40 (d) P(AC | F) = 0.40

(b) P(A | FC) = 0.40 (e) None of these

(c) P(F | AC) = 0.40

Step by step solution

01

Step 1. Given Information

A cocktail party was attended by $40\%$ of those who had food poisoning.

02

Step 2. Concept used

Conditional probability :$P\left(B\right|A)=\frac{P(AandB)}{P\left(A\right)}$

03

Step 3. Calculation

Let F stand for food poisoning and A for attending a party, as indicated in the question.

Above that a person has good poisoning, there is a $40\%$chance that person will attend the party, according to the given statement.

Alternatively, given F, there is a $40\%$chance that A will occur.

After the vertical line, the "given" events must be specified, and the other event must be mentioned before the vertical line.

As a result, the conditional probability can be expressed as:$P\left(A\right|F)=40\%=0.40$

The proper option, according to the option, is $\left(e\right)0.40$

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