Question

A, B, and C are mutually exclusive events such that $P\left(A\right)=0.2,P\left(B\right)=0.6,$and $P\left(C\right)=0.1$. Find $P(AorBorC)$.

Short answer

The probability of$P(AorBorC)=0.9$.

Step-by-step solution

Step 1. Given information.

The given statement is:

A, B, and C are mutually exclusive events such that$P\left(A\right)=0.2,P\left(B\right)=0.6,\mathrm{and}P\left(C\right)=0.1$

Step 2. Find P(A or B or C) .

If A and B are events, and they are mutually exclusive, it means:

$P(A\&B)=P(B\&C)=P(C\&A)=P(A\&B\&C)=0$

Therefore, the probability if events A, B, and C are mutually exclusive will become:

$$\begin{gathered} P\left(AorBorC\right)=P\left(A\right)+P\left(B\right)+P\left(C\right) \\ =0.2+0.6+0.1 \\ =0.9 \end{gathered}$$