union of two independent probabilistic event I have following question:
Suppose we have two independent events whose probability are the following: $P(A)=0.4$ and $P(B)=0.7$. 
We are asked to find $P(A \cap B)$ from probability theory. I know that $P(A \cup B)=P(A)+P(B)-P(A \cap B)$. But surely the last one is equal zero so it means that  result should be $P(A)+P(B)$ but it is more than $1$ (To be exact it is $1.1$). Please help me where i am wrong?
 A: If $A$ and $B$ are 2 independent events then : 
\begin{align*}
P(A \cup B) &= P(A) + P(B) - P(A)\cdot P(B) \quad \Bigl[\because \tiny P(A \cap B) = P(A) \cdot P(B) \ \text{for independent events} \Bigr] \\ &=  \frac{4}{10} + \frac{7}{10} - \frac{28}{100} \\ &= \frac{110-28}{100} = \frac{82}{100} =0.82
\end{align*}
Please refer this link:


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*http://www.proofwiki.org/wiki/Definition:Independent_Events
A: No, the last one is not $0$. If $A,B$ are independent, then $P(A \cap B) = P(A) P(B) = 0.4 \cdot 0.7 = 0.28$ 
A: All things considered, it is important to realize the great difference between mutually exclusive and independent events. This is what throws everybody off in my math class. Mutually exclusive is when two events cannot happen at the same time and independent is when two events do not influence each other. In this case, there is an intersection because there are independent events, so you would subtract 1/28. On the other hand, let's look at it this way. If A was the chance of picking a king (4 kings) from a deck of cards and B was the chance of picking a queen as a deck of cards (4 queens), what is the probability that you would pick a king or a queen. Well, obviously a card cannot have both a king and a queen, therefore, there would not be an intersection. Hope that makes sense!
A: If the events $A$ and $B$ are independent, then $P(A \cap B) = P(A) P(B)$ and not necessarily $0$.
You are confusing independent with mutually exclusive.
For instance, you toss two coins. What is the probability that both show heads? It is $\frac{1}{2} \times \frac{1}{2}$ isn't it? Note that the coin tosses are independent of each other.
Now you toss only one coin, what is the probability that it shows both heads and tails?
