# Two events A and B are such that P(A)=.2, P(B)=.3, and P(AuuB)=.4. What is P(AnnB)?

## If A and B are independent events with $P \left(A\right) = .5 \mathmr{and} P \left(B\right) = .2$, what is $P \left(A \cup B\right)$?

Jan 6, 2017

The answer is ${P}_{A \cap B} = 0.1$
THe answer is ${P}_{A \cup B} = 0.1$

#### Explanation:

${P}_{A} = 0.2$

${P}_{B} = 0.3$

${P}_{A \cup B} = 0.4$

${P}_{A \cup B} = {P}_{A} + {P}_{B} - {P}_{A \cap B}$

${P}_{A \cap B} = {P}_{A} + {P}_{B} - {P}_{A \cup B}$

Therefore,

${P}_{A \cap B} = 0.2 + 0.3 - 0.4 = 0.1$

If the events are independent

${P}_{A \cup B} = {P}_{A} \cdot {P}_{B} = 0.5 \cdot 0.2 = 0.1$