Question

determine whether the following statement is true or false. if it is false, rewrite it as a true statement.

if two events are independent, \\(p(a|b) = p(b)\\).

choose the correct answer below.

a. false; if events a and b are independent, then \\(p(b|a) = p(a)\\).
b. false; if events a and b are independent, then \\(p(a|b) = p(a)\\).
c. false; if events a and b are independent, then \\(p(a \text{ and } b) = 0\\).
d. true

Explanation:

Analyze the given statement

Using the Independent Events Probability and Conditional Probability Notation knowledge points

$$ \text{Statement: "If two events are independent, } P(A|B) = P(B)\text{."} $$

Define independence of events

Using the Independent Events Probability knowledge point

$$ \text{Events } A \text{ and } B \text{ are independent if } P(A|B) = P(A) \text{ or } P(B|A) = P(B). $$

Evaluate the statement and options

Using the Independent Events Probability knowledge point

$$
LATEXBLOCK0
$$

Answer:

• A. False; if events A and B are independent, then P(B|A) = P(A).
• B. False; if events A and B are independent, then P(A|B) = P(A). (Correct answer)
• C. False; if events A and B are independent, then P(A and B) = 0.
• D. True