Question

let a and b be independent events with ( p(a) = 0.38 ) and ( p(acap b)=0.31 ). calculate and find ( p(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.

Explanation:

Step1: Use the formula for independent events

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

Step2: Solve for \(P(B)\)

Given \(P(A) = 0.38\) and \(P(A\cap B)=0.31\), we can rearrange the formula to \(P(B)=\frac{P(A\cap B)}{P(A)}\).
Substitute the values: \(P(B)=\frac{0.31}{0.38}\).
Calculate \(\frac{0.31}{0.38}\approx0.8158\) (rounded to four decimal places).

Answer:

\(0.8158\)