Question

question 6 of 39
according to the venn diagram below and given that p(a) = .45 as well as p(b) = .4 what is p(a ∪ b) ?
venn diagram with rectangle, red circle a, blue circle b, overlapping region labeled .10
options: a. .65, b. .75, c. .95, d. .85

Explanation:

Step1: Recall the formula for union of probabilities

The formula for \( P(A \cup B) \) is \( P(A) + P(B) - P(A \cap B) \).

Step2: Identify the values

We know \( P(A) = 0.45 \), \( P(B) = 0.4 \), and from the Venn diagram, \( P(A \cap B)= 0.10 \).

Step3: Substitute the values into the formula

\( P(A \cup B)= 0.45 + 0.4 - 0.10 \)
\( P(A \cup B)= 0.75 \)

Answer:

B. .75