Can you pls help me with this maths question?

Question

If two probabilities are independant is the following true:
P(a u b) = P(a) + Pb) ?

Thanking you in advance.

Answer 1

That is not true for INDEPENDENT events - it's true for MUTUALLY EXCLUSIVE events.

The formula for p(a u b) is p(a) + p(b) - p(a n b); the only time the last term [p(a n b)] goes away is if the events are mutually exclusive because mutually exclusive events occur completely seperate of one another. An example of a mutually exclusive event would be the probability that today is Wednesday AND today is Thursday. They can never happen together so the last term - the intersection of the two - is 0.

With independent events, an intersection can occur. For instance, today being Wednesday and today raining would be independent events. They don't affect one another. As we both know, however, they CAN occur at the same time because there have been plenty of rainy Wednesdays.

In fact, with independent events, the p(a n b) is defined as:

p(a n b) = p(a) * p(b),

and so the union formula that you mentioned would look like this:

p(a u b) = p(a) + p(b) - p(a n b)
p(a u b) = p(a) + p(b) - p(a)*p(b).

I just wanted to make sure your terminology's correct. Despite what the first two answers say, your statement is wrong if the events are indeed independent.

See the below website if you need further help.

Answer 2

In general, no. This is only true if the 2 events
are mutually exclusive, i.e. when a ∩ b is empty.
The general formula is
p(a U B) = p(a) + p(b) - p(a ∩ b).
If 2 events are independent then
p(a ∩ b) = p(a) * p(b).

Answer 3

Yes.