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### High School Mathematics - 213.5 Combination of Two Events

#### Combination of two Events

1. Union of Events
If A and B are 2 events of sample space S then A U B ( or A+B ) is the event that either A or B or both take place.
2. Intersection of Events
If A and B are 2 events of sample space S then A Ç B (or AB ) is the event that both A and B take place.
3. Mutually Exclusive Events
Two events A and B are said to be mutually exclusive if they cannot occur simultaneously. In such case ( A Ç B) is a { } set.
4. Exhaustive Events
Two events are said to be Exhaustive if A U B = S (sample space)

P( A U B) = P(A) + P(B) - P( A Ç B)

Solved Example

A box contains 36 tickets numbered 1 to 36. One ticket is drawn at random. Find the probability that the number on the ticket is either divisible by 3 or is a perfect square.

Solution
n(S)= 36
Let A be the event that the number is divisible by 3.
A = { 3,6,9,12,15,18,21,24,27,30,33,36 }
n(A) = 12 P(A) = 12/36
Let B be the event that the number on the ticket is a perfect square.
P(B) = { 1,4,9,16,25,36 }
n(B) = 6
P(B) = 6/36
Now A Ç B = { 9, 36}
n( A Ç B )= 2
P( A Ç B ) = 2/36
The required probability is P(A U B)
P(A U B) = P(A) + P(B) - P( A Ç B)
= 12/36 + 6/36 -2/36
= 4/9

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