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A hospital receives two fifths of its flu vaccine from Company A and the remainder from
Chapter 1, Problem 1.5-13(choose chapter or problem)
A hospital receives two fifths of its flu vaccine from Company A and the remainder from Company B. Each shipment contains a large number of vials of vaccine. From Company A, 3% of the vials are ineffective; from Company B, 2% are ineffective. A hospital tests n = 25 randomly selected vials from one shipment and finds that 2 are ineffective. What is the conditional probability that this shipment came from Company A?
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QUESTION:
A hospital receives two fifths of its flu vaccine from Company A and the remainder from Company B. Each shipment contains a large number of vials of vaccine. From Company A, 3% of the vials are ineffective; from Company B, 2% are ineffective. A hospital tests n = 25 randomly selected vials from one shipment and finds that 2 are ineffective. What is the conditional probability that this shipment came from Company A?
ANSWER:Step 1 of 3
Let A be the event that shipment came from company A and B be the event that shipment came from company B.
Also, let F be the event that a vial is ineffective and E be the event that 2 vial from sample of 25 are ineffective.
To find the conditional probability that \(P(A \mid E)\).
From the given Information,
\(\begin{array}{l}
\begin{aligned}
P(A) & =\frac{2}{5} \\
& =0.4
\end{aligned}\\
\begin{aligned}
P(B) & =1-\frac{2}{5} \\
& =0.6
\end{aligned}\\
\begin{array}{l}
P(F \mid A)=0.03 \\
P(F \mid B)=0.02
\end{array}
\end{array}\)