Probability of (A Intersection B) = Probability of (A) ADD Probability of (B)

P(A or B) = P(A) + P(B) [NOTE: the symbol for the word 'or' in Maths is U, standing for Union. This means it can also be written as 'P(A U B) = P(A) + P(B)']

P(A u B) = P(A) + P(B) - P(A n B)

The probability of mutually exclusive events is:

P(AUB)=P(A)+P(B)

A (Intersection) B = {} or empty set(0)

P(A or B) = P(A) + P(B)

Mutually exclusive events are events that can not happen at the same time eg) you can't get a head and a tail when you toss a coin. When displayed on a venn diagram mutually exclusive events will not have an intersection and so

P(AuB) = P(A) + P(B)

Mutually exclusive events cannot happen at the same time. If the events are A and B then P(A∩B) = 0.

P (A or B) = P (A) + P (B)

The probability of two events that are mutually exclusive both occurring is simply the product of the individual events happening. This can also be expressed as

P(A & B) = P(A)*P(B)

This does not hold if A and B are not independent, in which case we need to take into account what happens to an event probability given the other event has caused it to changed. Let's say that we want to work out the probability of event A & B given under these circumstances.

P(A & B) = P(A)*P(B|A)

Notice the last term in the multiplication has changed. It basically means "Probability of B happening given A has already happened." Note that tree diagrams help a lot with this kinds of thinking!

However for mutually exclusive events, the first formula is the one you want!

The probability (P) of either event A or event B occurring, when the events are mutually exclusive, is calculated by adding their individual probabilities. Both events cannot occur at the same time hence their probabilities are not related to one another:

P(A or B)=P(A)+P(B)

This means the events cannot occur at the same time. So if you have 2 mutually exclusive events;

P(A or B) = P(A U B) = P(A) + P(B)

If two events A and B are mutually exclusive events, they have no common outcomes hence P(A intersection B) = 0

Mutually exclusive events are 2 or more events that cannot happen at the same time. This means the probability of them occurring is always 0.

A good example of this is a standard deck of cards: No card can be in two different suits, such as hearts and diamonds, so the probability of getting 1 single card with both hearts and diamonds will always be 0.

P(A∩B) = 0

The probability of A and B is zero as A and B are mutually exclusive events

Independence means the occurrence of one event(A) does not affect the probability of the others.(B).