FACTS  AND  FORMULAE  FOR  PROBABILITY  QUESTIONS

 

 

1. Experiment : An operation which can produce some well-defined outcomes is called an experiment.

 

2. Random Experiment :An experiment in which all possible outcomes are know and the exact output cannot be predicted in advance, is called a random experiment.

Ex :

i. Tossing a fair coin.

ii. Rolling an unbiased dice.

iii. Drawing a card from a pack of well-shuffled cards.

 

3. Details of above experiments:

i. When we throw a coin, then either a Head (H) or a Tail (T) appears.

ii. A dice is a solid cube, having 6 faces, marked 1, 2, 3, 4, 5, 6 respectively. When we throw a die, the outcome is the number that appears on its upper face.

iii. A pack of cards has 52 cards.

  • It has 13 cards of each suit, name Spades, Clubs, Hearts and Diamonds.
  • Cards of spades and clubs are black cards.
  • Cards of hearts and diamonds are red cards.

There are 4 honours of each unit. There are Kings, Queens and Jacks. These are all called face cards.

 

4. Sample Space: When we perform an experiment, then the set S of all possible outcomes is called the sample space.

Ex :

1. In tossing a coin, S = {H, T}

2. If two coins are tossed, the S = {HH, HT, TH, TT}.

3. In rolling a dice, we have, S = {1, 2, 3, 4, 5, 6}.

Event : Any subset of a sample space is called an event.

 

5. Probability of Occurrence of an Event : 

Let S be the sample and let E be an event.

Then, ES

P(E)=n(E)n(S)

6. Results on Probability :

i. P(S) = 1    ii. 0P(E)1   iii. P()=0

 

iv. For any events A and B we have : 

P(AB)=P(A)+P(B)-P(AB)

 

v. If A denotes (not-A), then P(A)=1-P(A)

Q:

The mean of distribution is 11 and the standard deviation is 5. What is the value of the coefficient variation?

A) 45.45% B) 35.35%
C) 25.25% D) 55.55%
 
Answer & Explanation Answer: A) 45.45%

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Probability
Exam Prep: Bank Exams

0 737
Q:

The mean of a distribution is 20 and the standard deviation is 4. What is the value of the coefficient variation?

A) 10% B) 20%
C) 40% D) 60%
 
Answer & Explanation Answer: B) 20%

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Probability
Exam Prep: Bank Exams

4 724
Q:

The mean of 20 observations is 19. One more observation is included and the new mean becomes 20. The 21st observation is

A) 20 B) 30
C) 40 D) 42
 
Answer & Explanation Answer: C) 40

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Probability
Exam Prep: Bank Exams

2 721
Q:

The mean of a distribution is 15 and the standard deviation is 5. What is the value of the coefficient variation?

A) 16.66% B) 66.66%
C) 33.33% D) 100%
 
Answer & Explanation Answer: C) 33.33%

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Probability
Exam Prep: Bank Exams

5 697
Q:

The mean of the data 2, 9, 9, 3, 6, 9, 4 is

A) 33/7 B) 6
C) 43/7 D) 7
 
Answer & Explanation Answer: B) 6

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Probability
Exam Prep: Bank Exams

6 675
Q:

The mean of a distribution is 18 and the standard deviation is 4.5. What is the value of the coefficient of variation?

A) 50% B) 25%
C) 100% D) 75%
 
Answer & Explanation Answer: B) 25%

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Probability
Exam Prep: Bank Exams

0 670
Q:

If the standard deviation of a population is 10, what would be the population variance?

A) 100 B) 30
C) 5 D) 20
 
Answer & Explanation Answer: A) 100

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Probability
Exam Prep: Bank Exams

3 647
Q:

X attempts 94 questions and gets 141 marks. If for every correct answer 4 marks is given, and for every wrong answer 1 mark is deducted, then the number of questions wrongly answered by X is __.

A) 45 B) 47
C) 57 D) 40
 
Answer & Explanation Answer: B) 47

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Probability
Exam Prep: Bank Exams

6 637