Question

suppose that e and f are two events and that n(e and f)=210 and n(e)=490. 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 \(N\), since \(P(A)=\frac{N(A)}{N(S)}\) (where \(N(S)\) is the total number of outcomes in the sample - space), we have \(P(F|E)=\frac{N(E\cap F)}{N(E)}\) (because the \(N(S)\) terms cancel out).

Step2: Substitute the given values into the formula

We are given that \(N(E\cap F) = 210\) and \(N(E)=490\). Substituting these values into the formula \(P(F|E)=\frac{N(E\cap F)}{N(E)}\), we get \(P(F|E)=\frac{210}{490}\).

Step3: Simplify the fraction

\(\frac{210}{490}=\frac{210\div70}{490\div70}=\frac{3}{7}\approx0.429\)

Answer:

\(0.429\)