Question

Given : P(A)=2/3, P(B)=30%. A and B are mutually exclusive events. Find P(A or B). a)25/35b)29/30c)11/30d)30

Answer 1

ANSWER:

b)29/30

STEP-BY-STEP EXPLANATION:

When two events are exclusive, we can apply the following formula:

$\begin{gathered} P\mleft(AorB\mright)=P(A)+P(B) \\ P(A)=\frac{2}{3} \\ P(B)=30\text{\% }=\frac{30}{100}=\frac{3}{10} \end{gathered}$

We replace and calculate the P(A or B):

$\begin{gathered} P(AorB)=\frac{2}{3}+\frac{3}{10}=\frac{2\cdot10+3\cdot3}{3\cdot10}=\frac{20+9}{30} \\ P(AorB)=\frac{29}{30} \end{gathered}$