Question

let \\(b\\) and \\(c\\) be two events such that \\(p(b) = 0.49\\) and \\(p(c) = 0.01\\).
do not round your responses. (if necessary, consult a list of formulas.)
(a) determine \\(p(b \cup c)\\), given that \\(b\\) and \\(c\\) are mutually exclusive.
(b) determine \\(p(b \cup c)\\), given that \\(b\\) and \\(c\\) are independent.

Explanation:

Calculate union for mutually exclusive events

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

$$
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$$

Calculate intersection for independent events

Using the Independent Events Probability knowledge point

$$ P(B \cap C) = P(B) \times P(C) = 0.49 \times 0.01 = 0.0049 $$

Calculate union for independent events

Using the Addition Rule of Probability knowledge point

$$ P(B \cup C) = P(B) + P(C) - P(B \cap C) = 0.49 + 0.01 - 0.0049 = 0.4951 $$

Answer:

(a) Determine \(P(B \cup C)\), given that \(B\) and \(C\) are mutually exclusive.
<blank>0.5</blank>

(b) Determine \(P(B \cup C)\), given that \(B\) and \(C\) are independent.
<blank>0.4951</blank>