Question

if e and f are events with ( p(e)=0.302 ), ( p(f)=0.283 ), and ( p(e cap f)=0.087 ), calculate ( p(e | 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: Substitute the given values into the formula

We are given \( P(E\cap F) = 0.087 \) and \( P(F)=0.283 \). So, \( P(E|F)=\frac{0.087}{0.283} \).

Step3: Perform the division

\( \frac{0.087}{0.283}\approx0.3074 \) (rounded to four decimal places as \( 0.087\div0.283 = 0.3074205\cdots\))

Answer:

\( 0.3074 \)