#### GATE Practice Questions - Engineering Mathematics Probability

# GATE Practice Questions - Engineering Mathematics Probability

GATE Practice Questions for Engineering Mathematics is a highly searched term by GATE aspirants on the web, so we have decided to share GATE Practice questions on important topics in GATE syllabus with the students. In this post, we will share the questions on the topic of Probability from the subject of Engineering Mathematics in GATE syllabus. Feel free to share your queries and doubts on the shared questions in the comment area or email us at info@mindvis.in.

**Q1) **Seven car accidents occurred in a week, what is the probability that they occurred on the same day?

**Sol) **Probability that car accident occurred on a particular day of the week=1/7

Probability that all 7 accidents occurred on a particular day of the week =

Required probability =

**Q2) **Four fair coins are tossed simultaneously, what is the probability that at least one heads and at least one tails turn up is

- 1/16
- 1/8
- 7/8
- 15/16

**Sol) **S = 16

Probability of all heads or all tails appearing = (1/16) + (1/16) = 1/8

Required probability = 1 - (1/8) = 7/8

**Q3) **Let p(E) denote the probability of an event E. Given p(A)=1 and p(B)= ½, then the value of p(A/B) and p(B/A) respectively are

- 1/4, 1/2
- 1/2, 1/4
- 1/2, 1
- 1, 1/2

**Sol) **P(A) = 1, P(B) = 1/2

**Q4) **A fair dice is rolled twice, the probability that an odd number will follow an even number is

- 1/2
- 1/6
- 1/3
- 1/4

**Sol) **P(even) = P(odd) = 1/2

Required probability = 1/2 x 1/2 = 1/4

**Q5) **The probability that there will be 53 Sundays in a randomly chosen leap year is,

- 1/7
- 1/14
- 1/28
- 2/7

**Sol) **1 leap year= 366 days i.e. 52 complete weeks and 2 more extra days, and the two days can be any of the following combinations i.e. Sun-Mon, Mon-Tue, Tue-Wed, Wed-Thu, Thu-Fri, Fri-Sat, and Sat-Sun

So the required probability is 2/7.

**Q6) **A random variable is uniformly distributed over the interval 2 to 10. The variance will be

- 16/3
- 256/9
- 6
- 36

**Sol) **

**Q7) **If a random variable X satisfies distribution the Poisson distribution with a mean value of 2, then the probability that that X>2 is

**Sol) **

**Q8) A box contains 2 washers, 3 nuts and 4 bolts. Items are drawn once at a time without replacement. The probability of drawing 2 washers first followed by by 3 nuts and subsequently the 4 bolts is**

- 2/135
- 1/630
- 1/1260
- 1/2520

**Sol) **Total number of items = 2 washers + 3 nuts +4 bolts = 9 items

Required probability = (2/9 x 1/8) x (3/7 x 2/6 x 1/5) x (4/4 x 3/3 x 2/2 x 1/1) = 1/1260

**Q9) **Two cards are drawn at random in succession with replacement from a deck of 52 well shuffled cards. Probability of getting both “Aces” is

- 1/169
- 2/169
- 1/13
- 2/13

**Sol) **P(selecting 1ACE card from a pack of 52 card) is = 4C_{1}/52C_{1}

P(two ACE with replacement) is = 4C_{1}/52C_{1} x 4C_{1}/52C_{1} = 1/169

**Q10)** A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is

- 0.0036
- 0.1937
- 0.2234
- 0.3874

**Sol) **Probability of defective item= 0.1

Probability of non-defective item= 0.9

Now two items can be selected in 10C_{2} ways

The required probability is = 10C_{2} x (0.1)^{2} x (0.9)^{8} = 0.1937