Question

the venn diagram shows event a and event b comprised of outcomes from the same sample space. the probability of event a is given, as well as the probability of neither event a nor event b. what is the probability of event b? a. 0.6 b. 0.4 c. 0.2 d. 0.5

Explanation:

Step1: Find the probability of neither A nor B

Let \(P(A) = 0.2\), \(P(\text{neither }A\text{ nor }B)=0.2\). The sum of all probabilities in the sample space is \(1\). Let \(P(B)=x\).
We know that \(P(A)+P(B)+P(\text{neither }A\text{ nor }B) = 1\).

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

Substitute the values into the equation: \(0.2 + x+0.2=1\).
Simplify the left - hand side: \(x + 0.4=1\).
Subtract \(0.4\) from both sides: \(x=1 - 0.4\).

Answer:

\(0.6\) (Option A)