No.  Problems & Solutions [Click Solution link to bring up the solutions page]  

01. 
If S denotes the sample space, then P(S) is
Solution Hide/Show
P(S) denotes the probability of occurrance of the sample space.
⇒ Probability of occurrence of at least one of the sample points This is a certainty. Thus P(S) = 1. Explanation
Consider the sample space consisting of "p" elementary events
Where "S" represents the sample space i.e. the set of all elementary events of the experiment. S = {e_{1}, e_{2}, e_{3}, ... , e_{p}} ⇒ n(S) = p


02. 
If sample space contains 10 equally likely simple events, then the probability of each simple event is
Solution Hide/Show
If there are 'n' elementary events (sample points) in an experiment all of which are equally likely and mutually exclusive, the probability of occurrence of each elementary event is equal to 1/n. Since there are 10 elementary events (sample points) in the experiment, the probabilty of occurrence of each elementary (sample point) is 1/10. Explanation
Consider the sample space consisting of the 10 elementary events
Where "S" represents the sample space i.e. the set of all elementary events of the experiment. S = {e_{1}, e_{2}, e_{3}, ... , e_{10}} ⇒ n(S) = 10 Let E_{1}, E_{2}, E_{3}, ... , E_{10} represent the events each with an elementary event as its sample points. Thus, E_{1} = {e_{1}} ⇒ n(E_{1}) = 1


03. 
The probability of an event containing 5 sample points in a sample space of 15 sample points is.
Solution Hide/Show
If there are 'n' elementary events (sample points) in an experiment all of which are equally likely and mutually exclusive, the probability of occurrence of each elementary event is equal to 1/n. Since there are 15 elementary events (sample points) in the experiment, the probabilty of occurrence of each elementary (sample point) is 1/15. Let "A" be the event consisting of the 5 sample points.
Explanation
Consider the sample space consisting of the 15 elementary events
Where "S" represents the sample space i.e. the set of all elementary events of the experiment. S = {e_{1}, e_{2}, e_{3}, ... , e_{15}} ⇒ n(S) = 15 Let E_{1}, E_{2}, E_{3}, ... , E_{15} represent the events each with an elementary event as its sample points. Thus, E_{1} = {e_{1}} ⇒ n(E_{1}) = 1
Let "A" be the event consisting of the 5 sample points.


04. 
S is a sample space. S = { x ∈ n/1 < x ≤ 100} and E = {x / (x+1) (x1) ∈ s}. then P(E) =
Solution Hide/Show
"S", the sample space is defined as {x ∈ n/1 < x ≤ 100} ⇒ S = {x ∈ n/1 < x ≤ 100} ⇒ S = {2, 3, 4, ... , 100} ⇒ n(S) = 99 Event "E", is defined as {x / (x+1) (x1) ∈ s} ⇒ E = {x / (x+1) (x1) ∈ s} ⇒ E = {2, 3, ... 10} ⇒ n(E) = 9 The probabilty of occurrence of the event "E"


05. 
If p(A) = 0, then A = Φ
Solution Hide/Show
Where "A" represents an event of the experiment whose sample space is "S".
Given P(A) = 0
⇒ n(A) = 0 Therefore, A = φ 

06. 
If s is a sample space containing 8 elements then the number of probability functions of s with co – domain { 0, 1} is
Solution Hide/Show
The event 

07. 
Describe explicity the sample spaces for each of the following experiments:
Solution Hide/Show
The event 

07. 
Describe sample space appropriate in each of the following cases:
Solution Hide/Show
The event 

08. 
Suppose an experiment has n out comes, A1, A2  An and that it is repeated r times. Let x1, x2  xn record the number of occurrence of A1, A2  An. describe the sample space. Show that the number of sample points is.
Solution Hide/Show
The event 

09. 
If A is an event of a sample space S, then the odds in favour of A are
The probability of sample space is
Solution Hide/Show
The event 

10. 
Let a sample space be S = [ a_{1}, a_{2}, a_{3}]. Which of the following defines probability space on S?
i) P(a_{1}) = 1/4, P(a_{2}) = 1/3, P(a_{3}) =1/3
Solution Hide/Show
The event 

11. 
A manufacturer buys parts from four different vendor’s numbered 1, 2, 3 and 4. referring to orders placed on two successive days (1,4) denotes the events that on the first day, the order was given to vendor 1 and on the second day it was given to vendor 4. letting A represent the event that vendor 1 gets at least one of these two orders, B the event that the same vendor gets at least one of these two orders, B the event that the same vendor gets both orders and C the event that vendors 1 and 3 do not get either order.
List the element of a) entire sample space (b) A (c) B (d) C (e)
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The event 

12. 
Let s be the samplw space and let A and B be the events. Find an expression for the events.
i) A or B occurs
Solution Hide/Show
The event 

13. 
Let S = { 1, 1/2, ... ... ... (1/2)^{n} } be a classical event space and A, B be events given by A = {1, 1/2} B = {(1/2)^{K} / k is an even positive integer}. Find p(
∩ )
Solution Hide/Show
The event 
No.  Problems for Practice 

01.  A coin is tossed three times in succession, the number of sample points in the sample space is? 
Author Credit : The Edifier 