Question

events a and b are disjoint. find p(a or b).

1. p(a) = 0.3, p(b) = 0.1
2. p(a) = \frac{2}{3}, p(b) = \frac{1}{5}

Explanation:

Problem 3

Step1: Recall disjoint events formula

For disjoint events \( A \) and \( B \), \( P(A \text{ or } B)=P(A)+P(B) \).

Step2: Substitute values

Given \( P(A) = 0.3 \) and \( P(B)=0.1 \), so \( P(A \text{ or } B)=0.3 + 0.1 \).

Step3: Calculate the sum

\( 0.3+0.1 = 0.4 \).

Step1: Recall disjoint events formula

For disjoint events \( A \) and \( B \), \( P(A \text{ or } B)=P(A)+P(B) \).

Step2: Substitute values

Given \( P(A)=\frac{2}{3} \) and \( P(B)=\frac{1}{5} \), find a common denominator (15) to add: \( \frac{2}{3}+\frac{1}{5}=\frac{10}{15}+\frac{3}{15} \).

Step3: Calculate the sum

\( \frac{10 + 3}{15}=\frac{13}{15} \).

Answer:

\( 0.4 \)

Problem 6