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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: There are 15 tickets bearing numbers from 1-15 . One ticket is drawn from the bag at random. Find the probability that the number on it is an even number or a multiple of 4.
9/11
1/3
1/4
7/15

Q 2: In a stationery shop the probability that a person asks for an ink pen is 0.8, the probability that he will ask for a gell pen is 0.7 and the probability that he will ask for both is 0.65. Find the probability that he will ask for either of them.
17/20
7/8
12/19
23/31

Q 3: 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.
18/47
7/36
11/12
23/36

Q 4: 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.
12/31
11/18
7/31
19/18

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