Question

select the correct answer.
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
0.2
b
0.2
a. 0.2
b. 0.4
c. 0.5
d. 0.6

Explanation:

Step1: Define total probability rule

The sum of probabilities of all outcomes in a sample space is 1. This means:
$$P(A) + P(B) + P(\text{neither } A \text{ nor } B) = 1$$

Step2: Identify given values

From the Venn diagram: $P(A) = 0.2$, $P(\text{neither } A \text{ nor } B) = 0.2$

Step3: Solve for $P(B)$

Rearrange the formula to isolate $P(B)$:
$$P(B) = 1 - P(A) - P(\text{neither } A \text{ nor } B)$$
Substitute the known values:
$$P(B) = 1 - 0.2 - 0.2 = 0.6$$

Answer:

D. 0.6