Question

suppose that e and f are two events and that n(e and f) = 460 and n(e) = 830. what is p(f|e)?
p(f|e) ≈ (round to three decimal places as needed )

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(F|E)=\frac{P(E\cap F)}{P(E)}\). In terms of counts, if \(N(E\cap F)\) is the number of elements in \(E\cap F\) and \(N(E)\) is the number of elements in \(E\), then \(P(F|E)=\frac{N(E\cap F)}{N(E)}\) (since \(P(A)=\frac{N(A)}{N(S)}\), and when we take the ratio \(\frac{P(E\cap F)}{P(E)}=\frac{\frac{N(E\cap F)}{N(S)}}{\frac{N(E)}{N(S)}}=\frac{N(E\cap F)}{N(E)}\)).

Step2: Substitute the given values

We are given that \(N(E\cap F) = 460\) and \(N(E)=830\). Substituting these values into the formula \(P(F|E)=\frac{N(E\cap F)}{N(E)}\), we get \(P(F|E)=\frac{460}{830}\).

Step3: Calculate the value

\(\frac{460}{830}\approx0.554\) (using a calculator to perform the division \(460\div830\)).

Answer:

\(0.554\)