Question

let a and b be independent events with p(a)=0.93 and p(b)=0.92. calculate and find p(a∩b)=? note: if your final answer has up to four decimal places, enter your answer in the box below without rounding it. but if your final answer has more than four decimal places, then round the number to four decimal places. question 7 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∪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.

Explanation:

Step1: Use the formula for independent events

For independent events \(A\) and \(B\), \(P(A\cap B)=P(A)\times P(B)\).

Step2: Substitute the given values

Given \(P(A) = 0.93\) and \(P(B)=0.92\), we have \(P(A\cap B)=0.93\times0.92\).

Step3: Calculate the product

\(0.93\times0.92=(1 - 0.07)\times(1 - 0.08)=1-(0.07 + 0.08)+0.07\times0.08=1 - 0.15+0.0056 = 0.8556\)

Answer:

\(0.8556\)