Question

question 10
3 pts
let e and f be the events in a sample space s such that ( p(e|f) = 0.342 ), ( p(f) = 0.686 ). calculate ( p(ecap f) =? )
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.

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(E|F)=\frac{P(E\cap F)}{P(F)}\).

Step2: Rearrange the formula to solve for \(P(E\cap F)\)

From \(P(E|F)=\frac{P(E\cap F)}{P(F)}\), we can get \(P(E\cap F)=P(E|F)\times P(F)\).

Step3: Substitute the given values

Given \(P(E|F) = 0.342\) and \(P(F)=0.686\), then \(P(E\cap F)=0.342\times0.686\).

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Answer:

\(0.2346\)