Question

if a and b are mutually exclusive, and if p(a) = 0.5 and p(b) = 0.2, what is p(a ∪ b)?
p(a ∪ b) = \square

Explanation:

Step1: Recall the formula for mutually exclusive events

For mutually exclusive events \( A \) and \( B \), the probability of their union is given by the formula \( P(A \cup B) = P(A) + P(B) \) because \( P(A \cap B) = 0 \) (they cannot occur at the same time).

Step2: Substitute the given values

We are given that \( P(A) = 0.5 \) and \( P(B) = 0.2 \). Substituting these values into the formula, we get \( P(A \cup B) = 0.5 + 0.2 \).

Step3: Calculate the result

Adding the two probabilities, \( 0.5 + 0.2 = 0.7 \).

Answer:

\( 0.7 \)