Probability MCQs

MCQs on Probability

Solve Probability Multiple-Choice Questions to prepare better for GATE. Learn more about Probability and Probability MCQs by checking notes, mock tests, and previous years’ question papers. Gauge the pattern of MCQs on Probability by solving the ones that we have compiled below for your practice:

Probability Multiple-Choice Questions

1. If we throw two dice simultaneously, what would be the probability that we get a 10 or 11?

a. 5/36

b. 5/12

c. 1/7

d. 1/3

Answer: (a) 5/36

2. We placed cards marked from 2 to 101 in a box and then mixed thoroughly. If we draw one card out of the box, what would be the probability that this number is a perfect cube?

a. 1/100

b. 3/100

c. 3/101

d. 3/99

Answer: (b) 3/100

3. Consider X to be a random variable that follows a random distribution with +1 mean and variance 4. Here, if Y is another normal variable that has a -1 mean and its variance is unknown, then what would be the standard deviation of Y if P(X ≤ -1) = (P ≥2)?

a. 1

b. 2

c. 3

d. 1.414

Answer: (a) 1

4. Let us take a continuous random variable that has a probability density function as:

f(t) = 1 – t of 0 ≤ t ≤ 1

f(t) = 1 + t of -1 ≤ t ≤ 0

What would be the standard deviation for a random variable?

a.

\(\begin{array}{l}\frac{1}{6}\end{array} \)

b.

\(\begin{array}{l} \frac{1}{3}\end{array} \)

c.

\(\begin{array}{l}\frac{1}{\sqrt{6}}\end{array} \)

d.

\(\begin{array}{l}\frac{1}{\sqrt{3}}\end{array} \)

Answer: (b)

\(\begin{array}{l}\frac{1}{3}\end{array} \)

5. In an examination paper, there are 150 MCQs carrying 1 mark each. Every question has 4 choices, and every incorrect answer fetches a negative 0.25 mark. If 1000 students choose random answers with uniform probability, then what would be the total number of expected marks that every student will obtain?

a. 0

b. 2550

c. 7525

d. 9375

Answer: (d) 9375

6. If we roll a six-faced dice a large number of times, then what would be the mean values of its outcomes?

a. 1.5

b. 2.5

c. 3.5

d. 4.5

Answer: (c) 3.5

7. We will draw three cards from a pack of 52 cards. What would be the probability that these cards are a jack, a queen, and a king?

a. 8/16575

b. 3/13

c. 64/2197

d. 16/5525

Answer: (d) 16/5525

8. If we randomly select a point in the X-Y plane with a uniform probability within a rectangle that has its corners at points (0,0), (1,0), (1,2), and (0,2). Here, what would be the expected value of p square if p refers to the length of the point’s position vector?

a. 5/3

b. 4/3

c. 1

d. 2/3

Answer: (a) 5/3

9. We pick a thermostat from a production unit randomly. If the probability that it is defective is 0.1, then the probability that 3 out of 10 thermostats picked randomly would be defective is:

a. 0.3

b. 0.107

c. 0.057

d. 0.001

Answer: (c) 0.057

10. What would be the probability of obtaining at least two sixes when we throw a fair dice 4 times?

a. 19/144

b. 425/432

c. 13/144

d. 125/432

Answer: (d) 125/432

11. The total number of accidents that occur in a factory per month follows the Poisson distribution with a 5.2 mean. What would be the probability that less than 2 accidents would occur in the factory in any randomly given month?

a. 0.029

b. 0.034

c. 0.039

d. 0.044

Answer: (b) 0.034

12. The security system of an IT company consists of 10 computers, and exactly 4 of these are working. To check if a system is actually functional, the officials pick four computers at random and inspect them (without replacement). The system will be considered functional if at least three out of the four inspected computers are working. If p is the probability that this system would be considered functional, then 100p would be:

a. 11.90

b. 12.90

c. 10.90

d. 13.90

Answer: (a) 11.90

13. A given box consists of 3 red balls and 4 white balls. We select two balls randomly in succession and then remove them from this box. If the first removed ball is white, then what would be the probability of the second ball being red?

a. 1/2

b. 1/3

c. 4/7

d. 3/7

Answer: (a) 1/2

14. If we toss an unbiased coin five times, where the outcome of every toss is either a tail or head, then what would be the probability of getting at least a single head?

a. 1/32

b. 13/32

c. 16/32

d. 31/32

Answer: (d) 31/32

15. We roll a fair six-sided dice once. In case the value comes to be 1, 2, or 3, we roll the dice once again. Here, what would be the probability of getting values whose sum is at least 6?

a. 10/21

b. 5/12

c. 2/3

d. 1/6

Answer: (b) 5/12

16. A company assembles mobile phones. Here, ‘a’ is the probability of a mobile phone’s faulty assembly. Thus, the company subjects each mobile assembled to a testing process. If the probability of getting a correct result for any mobile phone in this test is ‘b’, then what would be the probability of getting a faulty result in this test?

a. (1-b)a

b. ab

c. ab + (1-a) + (1-b)

d. (1-a)b

Answer: (c) ab + (1-a) + (1-b)

17. If P(E) denotes the probability of occurring an event E, then what would be the values of P(B/A) and P(A/B), respectively, if P(A) = 1/2 and P(B) = 1?

a. 1, 1/2

b. 1/2, 1

c. 1/2, 1/4

d. 1/4, 1/2

Answer: (a) 1, 1/2

18. If we roll a fair dice twice, then what would be the probability that we get a result where an even number follows an odd number?

a. 1/2

b. 1/3

c. 1/4

d. 1/6

Answer: (c) 1/4

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