Probability GATE Questions

A highly popular method used to prepare for the GATE Exam is to practise all the previous years’ GATE Questions to gain perfection. Candidates can practise, analyse and understand concepts while solving them. It will also help you strengthen your time management skills. We have attempted to compile, here in this article, a collection of GATE Questions on Probability.

Candidates are urged to practise these Probability GATE previous years’ questions to get the best results. Probability is an important topic in the GATE ECE question paper, and solving these questions will help the candidates to prepare more proficiently for the GATE exams. Therefore, candidates can find the GATE Questions for Probability in this article to solve and practise before the exams. They can also refer to these GATE previous year question papers and start preparing for the exams.

GATE Questions on Probability

1. 500 students are taking one or more courses out of chemistry, physics and mathematics. Registration records indicate course enrolment as follows: chemistry (329), physics (186), mathematics (295), chemistry and physics (83), chemistry and mathematics (217), and physics and mathematics (63), How many students are taking all 3 subjects?

(GATE ECE 2017 Set 2)

1. 37
2. 43
3. 47
4. 53

Answer (d)

2. Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place) ________.

(GATE ECE 2017 Set 1)

1. 0.027
2. 0.050
3. 0.27
4. 0.50

Answer (a)

3. The second moment of a Poisson-distributed random variable is 2. Then the mean of the random variable is ______.

(GATE ECE 2016 Set 1)

1. 0
2. 1
3. 5
4. 10

Answer (b)

4. Let the random variable X represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of X is _______.

(GATE ECE 2015 Set 2)

1. 5
2. 6
3. 10
4. 11

Answer (b)

5. In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random has a sibling is ______.

(GATE ECE 2014 Set 1)

1. 0.66
2. 0.066
3. 0.55
4. 0.055

Answer (a)

6. A fair dice is rolled twice. The probability that an odd number will follow an even number is ________.

(GATE ECE 2005)

1. ½
2. ⅙
3. ⅓
4. ¼

Answer (d)

7. Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is a 40% chance of getting a reservation in any attempt by a passenger, then the average number of attempts that passengers need to make to get a seat reserved is __________.

(GATE ECE 2017 Set 2)

1. 2.5
2. 3
3. 3.5
4. 4

Answer (d)

8. The probability of getting a ”head” in a single toss of a biassed coin is 0.3. The coin is tossed repeatedly till a ”head” is obtained. If the tosses are independent, then the probability of getting ”head” for the first time in the fifth toss is _______.

(GATE ECE 2016 Set 3)

1. 0.072
2. 0.72
3. 0
4. 1

Answer (a)

9. A fair die with faces {1,2,3,4,5,6} is thrown repeatedly till ′3′ is observed for the first time. Let X denote the number of times the dice is thrown. The expected value of X is _______.

(GATE ECE 2015 Set 3)

1. 5
2. 6
3. 10
4. 15

Answer (b)

10. Parcels from sender S to receiver R pass sequentially through two post offices. Each post office has a probability ⅕ of losing an incoming parcel, independently of all other parcels. Given that a parcel is lost, the probability that it was lost by the second post office is ________.

(GATE ECE 2014 Set 4)

1. 0.44
2. 0.5
3. 0
4. 1

Answer (a)

11. Let U and V be two independent zero-mean Gaussian random variables of variances ¼ and 1/9, respectively. Then the probability P(3V≥2U) is _________.

(GATE ECE 2013)

1. 4/9
2. ½
3. ⅔
4. 5/9

Answer (b)

12. A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is ________.

(GATE ECE 2012)

1. ⅓
2. ½
3. ⅔
4. ¾

Answer (c)

13. A fair coin is tossed independently four times. The probability of the event ”The number of times heads show up is more than the number of times tails show up” is _________.

(GATE ECE 2010)

1. 1/16
2. ⅛
3. ¼
4. 5/16

Answer (d)

14. An examination consists of two papers, paper 1 and paper 2. The probability of failing in paper is 0.3, and that in paper 2 is 0.2. Given that a student has failed in paper 2, the probability of failing in paper 1 is 0.6. The probability of a student failing in both the papers is _________.

(GATE ECE 2007)

1. 0.5
2. 0.18
3. 0.12
4. 0.06

Answer (c)

15. Let X∈{0,1} and Y∈{0,1} be two independent binary random variables. If P(X=0)=p

and P(Y=0)=q, then P(X+Y≥1) is equal to __________.

(GATE ECE 2015 Set 2)

1. pq + (1 – p)(1 – q)
2. pq
3. p(1 – q)
4. 1 – pq

Answer (d)