Question

A and B are events such that $P\left(A\right)=0.2,P\left(B\right)=0.6,\mathrm{and}P(A\&B)=0.1$. Find$P(AorB)$.

Short answer

$P\left(AorB\right)=0.7$

Step-by-step solution

Step 1. Given information.

The given statement is:

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

Step 2. Find P(A or B).

If there are two events Aand Bthen the probability of either A, B, or both occurring is P(A or B), and the likelihood of both A and Boccurring is P(A & B).

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

$$\begin{gathered} P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(A\&B\right) \\ =0.2+0.6-0.1 \\ =0.7 \end{gathered}$$