Question

question\
suppose $a$ and $b$ are mutually exclusive events, and that $p(a) = 0.22$ and $p(b) = 0.46$. find $p(a\text{ or }b)$.\
provide your answer below:

Explanation:

Step1: Recall the addition rule for mutually exclusive events

For mutually exclusive events \( A \) and \( B \), the probability of \( A \) or \( B \) occurring is given by the formula \( P(A \text{ OR } B)=P(A)+P(B) \). This is because mutually exclusive events cannot occur at the same time, so there is no overlap (i.e., \( P(A \text{ AND } B) = 0 \)), and the addition rule simplifies to the sum of their individual probabilities.

Step2: Substitute the given values into the formula

We are given that \( P(A)=0.22 \) and \( P(B)=0.46 \). Substituting these values into the formula \( P(A \text{ OR } B)=P(A)+P(B) \), we get:
\( P(A \text{ OR } B)=0.22 + 0.46 \)

Step3: Calculate the sum

Adding the two probabilities together: \( 0.22+0.46 = 0.68 \)

Answer:

\( 0.68 \)