Problem 1
 The probability of a certain event is
 The probability of an impossible event is
 If an event cannot happen, the probability of the event will be
 The probability of an event lies between the limits
 If P(A) = 1, then A is called
Solution
 1
 0
 0 [an impossible event]
 0 and 1
 A certain event
Problem 2
Which of the following are incorrect statements?
 P(J) = 0.0
 P(K) = 0.1
 P(L) = 1.0
 P(M) = 1.8
 P(N) = − 0.2
Solution
 TRUE
P(J) represents the probability of an impossible event.
 TRUE
The probability of an event lies between 0 and 1.
 TRUE
P(L) represents the probability of a certain event.
 FALSE
0 ≤ P(EVENT) ≤ 1. The probability of an event should lie between 0 and 1.
 FALSE
0 ≤ P(EVENT) ≤ 1. The probability of an event should lie between 0 and 1.
Problem 3
The probability of any event is always a proper fraction
Solution
A proper fraction is a fraction where the numerator is less than the denominator.
More specifically, a Proper fraction is a fraction of the form
, where P, Q > 0 and
< 1
Probability of occurrence of Event A
 =  Number of Favorable Choices for the Event  Total Number of Possible Choices for the Experiment 

Since
m ≤ n always,
is always a proper fraction
Exceptions
The events which are either impossible or certain form an exception to this rule.
Probability of an impossible event
The probability of an impossible event is 0, which is possible only when the numerator is equal to zero, in which case the fraction is not an improper fraction. Probability of a certain event
The probability of a certain event is 1, which is possible only when the numerator is equal to the denominator, in which case the fraction is not an improper fraction.
Problem 4
 Events are said to be equally likely if
By exhaustive events we mean
 Equally likely cases
 Not equally likely cases
 Containing all possible cases
 None of these
Solution
 Two or more events are said to be equally likely if their probability of occurrence is equal.
 3  Exhaustive events mean events which cover all the possible cases within them.
Problem 5
Solution
P(A)  =  1 − P(A) 
 =  1 − 
 =  
 =  
Problem 6
If E is any event and E, its complement, then P(E) + P(E) =
Solution
P(E) + P(E)  =  P(E) + [1 − P(E)] 
 =  P(E) + 1 − P(E) 
 =  1 
Problem 7
If P(A) = 0.05, P(B) = 0.15 then P(A) + P(B) is equal to ...
Solution
P(A) + P(B)  =  [1 − P(A)] + [1 − P(B)] 
 =  [1 − 0.05] + [1 − 0.15] 
 =  0.95 + 0.85 
 =  1.8 
Practice Problems