Question

let (a) and (b) be two events such that (p(a) = 0.62) and (p(b) = 0.14).

do not round your responses. (if necessary, consult a list of formulas.)

(a) determine (p(a \cup b)), given that (a) and (b) are independent.

(b) determine (p(a \cup b)), given that (a) and (b) are mutually exclusive.

Explanation:

Identify the given probabilities

Using the Probability of Events knowledge point

$$ P(A) = 0.62,\quad P(B) = 0.14 $$

Calculate union for independent events

Using the Independent Events Probability and Addition Rule of Probability knowledge points

$$
LATEXBLOCK0
$$

Calculate union for mutually exclusive events

Using the Mutually Exclusive Events and Addition Rule of Probability knowledge points

$$
LATEXBLOCK1
$$

Answer:

(a) \(0.6732\)

(b) \(0.76\)