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High School Mathematics - 2
13.5 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 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 B) is a { } set.
  4. Exhaustive Events
    Two events are said to be Exhaustive if A U B = S (sample space)

Addition Theorem

P( A U B) = P(A) + P(B) - P( A 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 B = { 9, 36}
n( A B )= 2
P( A B ) = 2/36
The required probability is P(A U B)
P(A U B) = P(A) + P(B) - P( A B)
= 12/36 + 6/36 -2/36
= 4/9


Q 1: 2 dice are rolled. Find the probability that the sum of the numbers on the uppermost face is an even number or a perfect square.
11/18
7/31
19/18
12/31

Q 2: There are 100 lottery tickets numbered from 1- 100 . One of them is drawn at random. What is the probability that it is a multiple of 5 or 7?
3/8
8/25
11/100
1/5

Q 3: In a coffee shop the probaility that a customer drinks Capuccino is 0.5 and that he drinks mocaccino is 0.4 and that he drinks something from each of them is 0.25. Find the probability that the customer drinks at least one of the two.
11/20
13/20
12/19
16/19

Q 4: 2 dice are rolled. Find the probability that the sum of the numbers on the uppermost faces is a prime number or a number greater than 8.
11/12
23/36
7/36
18/47

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