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Compound Events

A Compound Event is when two events are happening at one time.  In other words, you are looking for two things that are occurring at the same time. 

 

There are two categories of compound events, ones that are mutually exclusive (can not occur at the same time)

Mutually exclusive events are found by listing all possible outcomes and counting all the favorable outcomes that satisfy both events.  Both of the following events are mutually exclusive.

Example: Two spinners labeled 1, 2, 3 (evenly spaced) are spun.

a. Find the probability that the sum of the numbers is even and greater than 3.

b. Find the probability that the sum of the numbers  is either 3 or 5.

In all mutually exclusive events list all the possible outcomes:

(1,1) = 2    (1,2) = 3     (1,3) = 4

(2,1) = 3    (2,2) = 4     (3,3) = 5

(3,1) = 4    (3,2) = 5     (3,3) = 6   There are nine possible outcomes.

a) P(even sum and greater than 3) =  since the only sum that satisfies the condition of even and greater than three.

b) P(3 or 5) = P(3) + P(5)   - The P(3) = and the P(5) = so the P(3 or 5) =

 

Events that are not mutually exclusive can occur at the same time.  To find the probability of this happening you must add the probability of each event occurring and subtract out the number of times that they occur at the same time.

It can be found by P(A or B) = P(A) + P(B) - P(A and B)

 

Example: The above spinners are spun.  Find the probability that the sum is greater than three or even.

P(greater than 3 ) = and the P(even) =   The P(greater than  3 and even)=

P(greater than 3 or even) = + - =