Friday, 11 November 2016

AMCAT Previous Years Questions on Probablity

 Topics Sub- Topics Expected Ques Basic Mathematics 6 - 8 Questions Applied Mathematics 8 - 10 Questions Engineering Mathematics 8 - 10 Questions

Ques. 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 red, is:

Op 1: 1/22

Op 2: 3/22

Op 3: 2/91

Op 4: 2/77

Op 5:

Correct Op : 3

Ques. A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random

from this box. The probability that at least one of these is defective, is:

Op 1: 4/19

Op 2: 7/19

Op 3: 12/19

Op 4: 21/95

Op 5:

Correct Op : 2

Ques. In a class, 30% of the students offered English, 20% offered Hindi and 10% offered both. If a

student is selected at random, what is the probability that he has offered English or Hindi ?

Op 1: 2/5

Op 2: 3/4

Op 3: 3/5

Op 4: 3/10

Op 5:

Correct Op : 1

Ques. A box contains 6 red balls, 7 green balls and 5 blue balls. Each ball is of a different size. The

probability that the red ball being selected is the smallest red ball, is

Op 1: 1/18

Op 2: 1/3

Op 3: 1/6

Op 4: 2/3

Op 5:

Correct Op : 3

Ques. If A and B are 2 independent events and P(A)=0.5 and P(B) = 0.4, find P(A/B):

Op 1: 0.5

Op 2: 0.4

Op 3: 0.88

Op 4: None of these

Op 5:

Correct Op : 1

Ques. A 5-digit number is formed by the digits 1,2,3,4 and 5 without repetition. What is the probability

that the number formed is a multiple of 4?

Op 1: 1/4

Op 2: 1/5

Op 3: 2/5

Op 4: 1/120

Op 5: 4

Correct Op : 2

Ques. In a single throw of dice, what is the probability to get a number greater or equal to 4?

Op 1: 1/3

Op 2: 2/3

Op 3: 1/2

Op 4: None of these

Op 5:

Correct Op : 3

Ques. A bag contains 5 oranges, 4 bananas and 3 apples. Rohit wants to eat a banana or an apple. He

draws a fruit from the bag randomly. What is the probability that he will get a fruit of his choice?

Op 1: 3.5/12

Op 2: 7/12

Op 3: 5/12

Op 4: None of these

Op 5:

Correct Op : 2

Ques. There are two boxes A and B. Box A has three red and four blue balls. Box B has five red and two

blue balls. Anya draws a ball from each bag randomly. What is the probability that both balls are red?

Op 1: 4/7

Op 2: 8/49

Op 3: 7/8

Op 4: 15/49

Op 5:

Correct Op : 4

Ques. Ravi has a bag full of 10 Nestle and 5 Cadbury chocolates. He draws two chocolates. What is the

probability that he got at least one Nestle chocolate?

Op 1: 2/3

Op 2: 3/7

Op 3: 2/21

Op 4: None of these

Op 5:

Correct Op : 4

Ques. The probability of having at least one tail in 5 throws of a coin is

Op 1: 1/32

Op 2: 31/32

Op 3: 1/5

Op 4: None of these

Op 5:

Correct Op : 2

Ques. A bag contains 5 yellow and 4 brown pencils. If two pencils are drawn, what is the probability that

the pencils are of the same colour?

Op 1: 5/108

Op 2: 1/6

Op 3: 5/18

Op 4: 4/9

Op 5:

Correct Op : 4

Ques. A single letter is drawn at random from the word, "ASPIRATION", the probability that it is a vowel

is?

Op 1: 1/2

Op 2: 1/3

Op 3: 3/5

Op 4: 2/5

Op 5:

Correct Op : 1

Ques. The probability that a man can hit a target is 3/4. He tries 5 times. The probability that he will hit

the target at least three times is:

Op 1: 291/364

Op 2: 371/464

Op 3: 471/502

Op 4: 459/512

Op 5:

Correct Op : 4

Ques. An unbiased dice is rolled 3 times. The probability that the value on the dice is not more than 4 in

any of the 3 rolls is:

Op 1: 8/27

Op 2: 1/27

Op 3: 26/27

Op 4: 2/3

Op 5:

Correct Op : 1

Ques. Probability of occurrence of event A is 0.5 and that of event B is 0.2. The probability of occurrence

of both A and B is 0.1. What is the probability that none of A and B occur?

Op 1: 0.3

Op 2: 0.4

Op 3: 0.7

Op 4: None of these

Op 5:

Correct Op : 2

Ques. An unbiased coin is tossed 5 times. If tail appears on first four tosses, then probability of tail

appearing on the fifth toss is:

Op 1: 1/2

Op 2: 1

Op 3: 0

Op 4: 4/5

Op 5:

Correct Op : 1

Ques. X and Y are two independent events. The probability that X and Y occur is 1/12, and the

probability that neither occur is 1/2, the probability of occurrence of X can be:

Op 1: 1/3

Op 2: 1/5

Op 3: 1/2

Op 4: 1/10

Op 5:

Correct Op : 1

Ques. An unbiased coin is tossed n times. If the probability of getting 4 tails equals the probability of

getting 7 tails, then the probability of getting two tails is:

Op 1: 55/2048

Op 2: 3/4096

Op 3: 1/1024

Op 4: None of these

Op 5:

Correct Op : 1

Ques. Sudhanshu and Pankaj stand in a circle with 10 other persons. If the arrangement of the person is

at random, then the probability that there are exactly 3 persons between Sudhanshu and Pankaj is?

Op 1: 9/11

Op 2: 2/11

Op 3: 1/11

Op 4: None of these

Op 5:

Correct Op : 2

Ques. Three numbers are chosen from 1 to 30 randomly. The probability that they are not consecutive

is:

Op 1: 1/145

Op 2: 144/145

Op 3: 139/140

Op 4: 1/140

Op 5:

Correct Op : 2

Ques. A bag is full of 20 bananas and no other fruit. Rajeev draws a fruit from the bag. What is the

probability that he will draw a banana?

Op 1: 1

Op 2: 0

Op 3: 1/2

Op 4: None of these

Op 5:

Correct Op : 1

Ques. An unbiased dice is rolled 5 times and the outcomes are 1, 2, 3, 4 and 5 respectively. If it is rolled

again, what is the probability that the outcome is 6?

Op 1: 1

Op 2: 5/6

Op 3: 1/6

Op 4: None of these

Op 5:

Correct Op : 3

Ques. The probability of drawing an apple from a bag of fruits is 6/25. How many apples should Ravi

draw, so that there is a chance he will draw 12 apples on average?

Op 1: 25

Op 2: 50

Op 3: 12

Op 4: None of these

Op 5:

Correct Op : 2

Ques. What is the probability for a day to be Sunday?

Op 1: 1/7

Op 2: 1/5

Op 3: 52/365

Op 4: None of these

Op 5:

Correct Op : 1

Ques. Rani has a bag with three blue and three yellow coins. She takes out a coin, sees its colour and

puts it back in the bag. She does this thrice. What is the probability that she saw all blue coins.

Op 1: 1/8

Op 2: 1/2

Op 3: 1/3

Op 4: None of these

Op 5:

Correct Op : 1

Ques. Shikhar has a bag with 2 balls, each of which can be black or white with equal probability. Now, he

draws out a ball and it turns out to be black. After this event, what is the probability that both balls are

black?

Op 1: 1/2

Op 2: 1/4

Op 3: 1

Op 4: None of these

Op 5:

Correct Op : 1

Ques. A coin is tossed thrice. What is the probability that the first toss of coin lands head, second tail

and third lands tail as well?

Op 1: 1/16

Op 2: 3/8

Op 3: 1/8

Op 4: None of these

Op 5:

Correct Op : 3

Ques. The probability of occurrence of event A is 0.3 and that of event B is 0.4. The events are

independent. What is the probability of occurrence of both A and B?

Op 1: 0.7

Op 2: 0.1

Op 3: 0.12

Op 4: Cannot be determined

Op 5:

Correct Op : 3

Ques. The probability of occurrence of event A is 0.1 and that of event B is 0.2. The events are mutually

exclusive. What is the probability of occurrence of both A and B?

Op 1: 0.1

Op 2: 0

Op 3: 1

Op 4: Cannot be determined

Op 5:

Correct Op : 2

Ques. The probability of occurrence of event X is 0.8 and that of event Y is 0.05. The events are mutually

exclusive. What is the probability of occurrence of either X or Y?

Op 1: 0.85

Op 2: 0.75

Op 3: 0

Op 4: Cannot be determined

Op 5:

Correct Op : 1

Ques. A biased die has a probability of 1/4 of showing a 5, while the probability of any of 1, 2, 3, 4, or 6

turning up is the same . If three such dice are rolled, what is the probability of getting a sum of atleast 14

without getting a 6 on any die ?

Op 1: 5/24

Op 2: 9/160

Op 3: 1/30

Op 4: 7/160

Op 5:

Correct Op : 4

Ques. A, B, C, D and E play the following game. Each person picks one card from cards numbered 1

through 10. The person who picks the greatest numbered card loses and is out of the game. Now the

remaining four return their cards to the pack and draw again, and

Op 1: 3/14

Op 2: 4/17

Op 3: 1/5

Op 4: 5/24

Op 5:

Correct Op : 3