If two events a and b are mutually exclusive, what does the special rule of addition state?

Solution:

If two events say, a and b are mutually exclusive, it implies that if event a takes place then b cannot.

An example of such an event is the tossing of a single fair coin.

For a given toss either heads will appear or tails, both cannot.

The general addition rule of probabilities of any two events is stated as 

P(a or b) = P(a) + P(b) - P(a and b) --- (1)

Where,

P(a) = Marginal Property of event a, P(b) = Marginal property of event b, P(a and b) = joint probability of a and b

Case A: Let us apply the general rule:

What is the probability that when a card is drawn from a pack of playing cards it is a queen or a spade?

We can apply equation above here:

P(Queen or Spade) = P(Queen) + P(Spade) - P(Queen & Spade)

= 4/52 + 13/52 - 1/52

= (4 + 13 -1)/52

= 16/52

= 4/13

When a and b are mutually exclusive:

P(a and b) = 0

Hence the general rule of addition (in equation 1 above) is modified as follows

P(a or b) = P(a) + P(b)

P(Heads or Tails) = P(heads) + P(Tails) - P(Heads and Tails)

= 1/2 + 1/2 - 0

= 1

The interpretation is that if a fair coin is tossed it will certainly give either a heads or a tail.

Therefore, if two events a and b are mutually exclusive, the special rule of addition stated as follows: P(a or b) = P(a) + P(b)

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If two events a and b are mutually exclusive, what does the special rule of addition state?

Summary:

If two events a and b are mutually exclusive, the special rule of addition stated as follows: P(a or b) = P(a) + P(b)