Aptitude Probability

Probability

Probability: A mathematically measure of uncertainty is known as probability.

Random Experiment: An experiment in which all possible outcomes are known and exact

Outcome can be not be predicted, is called a random experiment.

Eg. Rolling an unbiased dice has all six outcomes (1, 2, 3, 4, 5, 6 ) known but exact outcome can be predicted.

Outcome: The result of a random experiment is called an outcome.

Sample Space: The set of all possible outcomes of a random experiment is known as sample space.

eg . The sample space in throwing of a dice is the set (1, 2, 3, 4, 5, 6)

Trial : The performance of a random experiment is called a trial.

eg. The tossing of a coin is called trial

Event: An event is a set of experimental outcomes, or in other words it is a subset of sample space.

eg. On tossing of a dice, let A denotes the event of even number appears on top A: { 2, 4, 6 }

Mutually Exclusive Events : Two or more events are said to be mutually exclusive if the occurrence of any one excludes the happening of other in the same experiment.

eg. On tossing of a coin it head occur, then it prevents happing of tail, in the same single experiment.

Exhaustive Events : All possible outcomes of an event are known as exhaustive events.

eg. In a through of single dice the exhaustive events are six { 1, 2, 3, 4, 5, 6 }

Equally Likely Event : Two or more events are said to be equally likely if the chances of their happening are equal.

eg. In throwing of an unbiased coin, result of Heat and Tail is equally likely.

Playing Cards:

(1) Total number of card are 52.

(2) There are 13 cards of each suit named Diamond, Hearts, Clubs and Spades

(3) Out of which Hearts and diamonds are red cards.

(4) Spades and Clubs are black cards

(5) There are four face cards each in number four Ace, King, Queen and Jack

Black Suit Card- (26)

i) Spade (13)

ii) Club (13)

Red Suit Card–(26)

i) Diamond (13)

ii) Heart (13)

(6) Each Spade, Club, Diamond, Heart has 9 digit cards 2, 3, 4, 5, 6, 7, 8, 9 and 10

(7) There are 4 Honors cards each Spade, Club, Diamond, Heart contains 4 numbers of Honours cards Ace, King, Queen and Jack

Quiz

TIME: (3-5) min

1. A bag contains 12 white and 18 black balls. Two balls are drawn in succession without replacement. What is the probability that first is white and second is black?

A) 36/135

B) 36/145

C) 18/ 91

D) 30/91

E) None of these

2. Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

A) 3/16

B) 1/8

C) 3/4

D) 1/2

E) None of these

3. In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected is:

A) 21/46

B) 21/135

C) 42/135

D) Can’t be determined

E) None of these

4. A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is?

A) 3/26

B) 3/52

C) 1/26

D) 1/4

E) None of these

5. A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are blue, is:

A) 1/91

B) 2/91

C) 3/91

D) 4/91

E) None of these.

6. A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

A) 5/7

B) 1/21

C) 10/21

D) 2/9

E) None of these

7. Three coins are tossed. What is the probability of getting at most two tails?

A) 1/8

B) 5/8

C) 3/8

D) 7/8

E) None of these

8. One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?

A) 1/13

B) 2/13

C) 3/13

D) 3/52

E) None of these

9. P and Q sit in a ring arrangement with 10 persons. What is the probability that P and Q will sit together?

A) 2/11

B) 3//11

C) 4/11

D) 5/11

E) None of these

10. Two dice are thrown simultaneously. Find the probability of getting a multiple of 2 on one dice and multiple of 3 on the other dice.

A) 1/9

B) 11/36

C) 13/36

D) Data inadequate

E) None of these

Answers

1. B

2. C
3. A
4. C
5. D
6. C
7. D
8. C
9. A
10.B

Explanation:

1. The probability that first ball is white= 12c1/30c1= 2/5
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence the probability the second ball is black= 18c1/29c1 =18/29
Required probability = 2/5*18/29 = 36/145

2. In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.
Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4),
(3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),
(6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
n(E) = 27.
so probability = 27/36 = 3/4

3. Probability = 10c1*15c2/25c3
= 21/46

4. 2/52 = 1/26

5. 6c3/15c3 =4/91

6. 5c2/7c2 = 10/21

7. 7/8

8. 12/52 =3/13

9. n(S)= number of ways of sitting 12 persons at round table:
=(12-1)!=11!
Since two persons will be always together, then number of persons:
=10+1=11
So, 11 persons will be seated in (11-1)!=10! ways at round table and 2 particular persons will be seated in 2! ways.
n(A)= The number of ways in which two persons always sit together =10!×2
So probability = 10!*2!/11!= 2/11

10. 11/36