GATE · Engineering Mathematics

Probability

15 practice questions, each with the answer and an explanation.

Practise Probability now

Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 15 questions

A continuous random variable $X$ has the probability density function $f (x) = \frac{3}{4} x (2 - x)$ for $0 \leq x \leq 2$ , and $0$ elsewhere. What is the conditional probability $P (X > 1 ∣ X > 0.5)$ ?
Two fair dice are thrown. What is the probability that the sum of the numbers is $7$ ?
Two fair dice are thrown. What is the probability that the sum of the numbers is $9$ ?
Two fair dice are thrown. What is the probability that the sum of the numbers is $4$ ?
Two fair dice are thrown. What is the probability that the sum of the numbers is $10$ ?
Two fair dice are thrown. What is the probability that the sum of the numbers is $11$ ?
Two fair dice are thrown. What is the probability that the sum of the numbers is $5$ ?
If $A$ and $B$ are independent events with $P (A) = 3/4$ and $P (B) = 2/3$ , find $P (A \cap B)$ .
If $A$ and $B$ are independent events with $P (A) = 2/5$ and $P (B) = 1/2$ , find $P (A \cap B)$ .
A machine produces bolts with a 2% defect rate. In a random sample of 100 bolts, what is the probability of finding exactly 2 defective bolts using the Poisson approximation?
Two fair six-sided dice are rolled simultaneously. Given that the sum of the numbers is greater than 8, what is the conditional probability that the numbers are equal?
A continuous random variable X has probability density function f(x) = k * x^2 for 0 ≤ x ≤ 2, and 0 elsewhere. What is the expected value E[X]?
In a communication system, bit 0 is transmitted with probability 0.6 and bit 1 with 0.4. Due to channel noise, a transmitted 0 is received as 1 with probability 0.1, and a transmitted 1 is received as…
If X and Y are independent random variables each uniformly distributed on [0, 1], what is the probability P(X + Y ≤ 1)?
The variance of a binomial random variable with parameters n = 100 and p = 0.2 is:

Keep practising

Probability in other exams

Ready for the full GATE test?

Take a mock test GATE hub