Quoted from a popular book,
For instance, if we flip a fair coin twice, knowing whether the first flip is Heads gives us no information about whether the second flip is Heads. These events are independent.
On the other hand, knowing whether the first flip is Heads certainly gives us information about whether both flips are Tails. (If the first flip is Heads, then definitely it’s not the case that both flips are Tails.) These two events are dependent.
Mathematically, we say that two events E and F are independent if the probability that they both happen is the product of the probabilities that each one happens:
P(E,F) = P(E)P(F)
In the example above, the probability of “first flip Heads” is 1/2, and the probability of “both flips Tails” is 1/4, but the probability of “first flip Heads and both flips Tails” is 0.
QUESTION: In the example we say
P(first flip Heads) = 1/2 P(both flips Tails) = 1/4 P(first flip Heads and both flips Tails) = 1/2 * 1/4 (WHY NOT THIS?) P(first flip Heads and both flips Tails) = 0 (CORRECT ANSWER)
Although it makes logical sense to put zero, but doesn't explain why doesn't it fit the formula