Question

s2 l1 1. events a and b are mutually exclusive. calculate the missing probability p(a)=2/7 p(b)=1/7 p(a∪b)=? 1/7 10/7 3/7 s2 l1 2. determine if the events a and b are mutually exclusive. p(a)=3/5 p(b)=1/5 p(a∪b)=4/5 mutually exclusive not mutually exclusive

Explanation:

Step1: Recall probability formula for mutually - exclusive events

For mutually - exclusive events \(A\) and \(B\), \(P(A\cup B)=P(A)+P(B)\).

Step2: Substitute given values for first problem

Given \(P(A)=\frac{3}{5}\), \(P(B)=\frac{1}{5}\), then \(P(A\cup B)=\frac{3}{5}+\frac{1}{5}=\frac{3 + 1}{5}=\frac{4}{5}\), so \(A\) and \(B\) are mutually exclusive.

Step3: Substitute given values for second problem

Given \(P(A)=\frac{2}{7}\), \(P(B)=\frac{1}{7}\), then \(P(A\cup B)=P(A)+P(B)=\frac{2}{7}+\frac{1}{7}=\frac{2 + 1}{7}=\frac{3}{7}\)

Answer:

For the first part: Mutually Exclusive
For the second part: \(\frac{3}{7}\)