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Chapter 4: Problem 71

Given that \(A\) and \(B\) are two mutually exclusive events, find \(P(A\) or \(B\) ) for the following. a. \(P(A)=.71\) and \(P(B)=.03\) b. \(P(A)=.44\) and \(P(B)=.38\)

Short Answer

Expert verified
a. The probability of either event A or B occurring is 0.74. b. The probability of either event A or B occurring is 0.82.

Step by step solution

01

Understand the problem and identify given

We're given two mutually exclusive events A and B and their respective probabilities. For part a, those are \(P(A) = 0.71\) and \(P(B) = 0.03\). For part b, they are \(P(A) = 0.44\) and \(P(B) = 0.38\).
02

Apply the formula for the probability of either of two mutually exclusive events

The formula is \(P(A \cup B) = P(A) + P(B)\). Plug in the given probabilities into this formula.
03

Solve for \(P(A \cup B)\) (a. \(P(A)=.71\) and \(P(B)=.03\))

For part a, \(P(A \cup B) = P(A) + P(B) = 0.71 + 0.03 = 0.74\).
04

Solve for \(P(A \cup B)\) (b. \(P(A)=.44\) and \(P(B)=.38\))

For part b, \(P(A \cup B) = P(A) + P(B) = 0.44 + 0.38 = 0.82\).

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