Question

If $A$ and $B$ are independent events, $P\left(A\right)=0.1$ and $P\left(B\right)=0.9$, then $P(A\cup B)=$ ____

• A. $0.91$
• B. $0.09$
• C. $0.99$
• D. $0.90$

Answer 1

Answer: (A)

$0.91$

Since A and B are independent events so $P(A\cap B)=P\left(A\right)\times P\left(B\right)=0.1\times 0.9=0.09$

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$P\left(A\right)=0.1$

$P\left(B\right)=0.9$

$P(A\cap B)=0.09$

So

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$P(A\cup B)=0.1+0.9-0.09$

$P(A\cup B)=1-0.09=0.91$