Question

question 7
3 pts
let e and f be the events in a sample space s for which ( p(e)=0.425 ), ( p(f)=0.584 ), and ( p(e cup f)=0.78 ). calculate ( p(f | e)=? )
note: for any final answer that has up to four decimal places, enter your answer in the box below without rounding the number. for any answer with more than four decimal values, round your final answer to four decimal places.
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Explanation:

Step1: Find \(P(E\cap F)\)

Use the formula \(P(E\cup F)=P(E)+P(F)-P(E\cap F)\).
So, \(P(E\cap F)=P(E)+P(F)-P(E\cup F)\).
Substitute \(P(E) = 0.425\), \(P(F)=0.584\), and \(P(E\cup F)=0.78\) into the formula:
\(P(E\cap F)=0.425 + 0.584-0.78\)
\(P(E\cap F)=0.229\)

Step2: Calculate \(P(F|E)\)

Use the formula for conditional probability \(P(F|E)=\frac{P(E\cap F)}{P(E)}\).
Substitute \(P(E\cap F) = 0.229\) and \(P(E)=0.425\) into the formula:
\(P(F|E)=\frac{0.229}{0.425}\)
\(P(F|E)=0.5388235294\approx0.5388\)

Answer:

\(0.5388\)