Question

use the drawing tool(s) to form the correct answer on the provided number line. event a and event b are independent events. two probabilities associated with those events are shown below. p(a) = 0.4 p(a and b) = 0.14 calculate p(b) and place its value on the number line.

Explanation:

Step1: Recall the formula for independent events

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

Step2: Rearrange the formula to solve for \(P(B)\)

We can rewrite the formula as \(P(B)=\frac{P(A\cap B)}{P(A)}\).

Step3: Substitute the given values

Given \(P(A) = 0.4\) and \(P(A\cap B)=0.14\), then \(P(B)=\frac{0.14}{0.4}\).

Step4: Calculate the value of \(P(B)\)

\(P(B)=\frac{0.14}{0.4}= 0.35\)

Answer:

0.35