JEE Advanced Probability & Statistics — practice questions
82 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Advanced Probability & Statistics in the app →From a standard deck of 52 playing cards, what is the probability of drawing a heart?When a single die is thrown once, the sample space isFor any two events $A$ and $B$, the probability that exactly one of them occurs isIf $A$ and $B$ are mutually exclusive events, then the addition theorem reduces toIn a binomial setting with $n$ independent Bernoulli trials, probability of success $p$, and failure probabiliA sequence of trials is called Bernoulli trials if the trials areWhich formula correctly gives the variance of a discrete random variable $X$?For a discrete random variable $X$ taking values $x_i$ with probabilities $p_i$, the mean $E(X)$ is given byBayes' theorem is primarily used toLet $E_1,E_2,\ldots,E_n$ be mutually exclusive cases that cover the sample space. According to the theorem of Events $A$ and $B$ are independent. If $P(A)=0.3$ and $P(B)=0.5$, what is $P(A\cap B)$?If $P(A)=0.5$ and $P(B/A)=0.4$, then by the multiplication theorem, $P(A\cap B)$ equalsWhich property of conditional probability is correct?If events $A$ and $B$ satisfy $P(B)\neq 0$, which expression correctly defines the conditional probability of A fair coin is tossed twice. How many outcomes are there in the sample space?A fair six-sided die is rolled once. What is the probability of getting an even number?Two fair dice are rolled simultaneously. What is the probability that the sum of the numbers on the two dice iA card is drawn at random from a standard $52$-card deck. What is the probability that the card is either a ki$ in(180° - \theta)$ equals:$ in^2\theta + \cos^2\theta$ equals:$ in(A + B) = $sin(0°) equals:cos(90°) equals:sin²θ + cos²θ equals:tan(45°) equals:In which quadrant is sin θ positive and cos θ negative?sin(A + B) equals:If tan θ = 1/2 (acute), find sin 2θ:If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):The arithmetic mean of n values x1, x2, ..., xn is:Median of an odd-length sorted data set is:Probability of a certain event:Probability of rolling a 6 on a fair die:For independent events A and B, P(A and B) equals:Mode of data set is:For random variable X uniform on [0, 1]: E(X²) =E[X² + Y²] when X, Y are independent identically distributed with E(X) = 0, Var(X) = σ²:At least one '6' in 4 throws of a fair die:For two events A and B, P(A | B) = 0.6, P(B) = 0.5, P(A) = 0.4. P(B | A) =Mean Absolute Deviation (MAD):Two independent X, Y with Var(X) = 4, Var(Y) = 9. Var(X + Y) =For two events $A$ and $B$, which formula correctly gives the probability of $A\cup B$?
=0.3$, $P(B)=0.4$ and A, B are mutually exclusive, then $P(A\cup B)$ is:The probability of getting a number greater than 4 on a single throw of a die is:The identity $1 + \tan^2\theta$ equals:The period of the function $ in x$ is:The radian measure of $45^\circ$ is:The value of $ in\dfrac{\pi}{6}$ is:The expansion of $ in(A+B)$ is:The maximum value of $3 in\theta$ is:The value of $\cos 180^\circ$ is:An angle of $90^\circ$ in radians is:The value of $ in(\pi/4)$ is:The identity $ in 2A$ equals:The general solution of $\cos x = 1/2$ is:A fair coin is tossed twice. The probability of getting at least one head is:If $P(A) = 0.5, P(B) = 0.4, P(A \cap B) = 0.2$, then $P(A | B)$ is:Two events $A$ and $B$ are independent if:A binomial random variable $X$ has $n = 10$ trials and success probability $p = 0.3$. Its mean is:A card is drawn from a deck of 52. Given that the card is RED, what is the probability that it's a KING?If P(A) = 0.5, P(B) = 0.6, and P(A ∩ B) = 0.2, then P(A ∪ B) is:Two dice are rolled. The probability of getting AT LEAST ONE SIX is:Bayes' theorem is essentially used to:For a discrete random variable X with values 0, 1, 2 and probabilities 0.3, 0.5, 0.2 respectively, the mean E(In a binomial distribution B(n=10, p=0.5), the probability of EXACTLY 6 successes is:The 4 conditions required for a binomial distribution (Bernoulli trials) include all the following EXCEPT:For a binomial distribution B(n, p), the MEAN and VARIANCE are:The number of ways to choose 3 books out of 5 (order does NOT matter) is:The angle 90° in radians is:The fundamental Pythagorean identity in trigonometry is:The exact value of cos 60° is:The double angle formula sin 2A equals:The general solution of sin θ = 1/2 is:The principal value range of sin⁻¹(x) is:In a triangle ABC, the Law of Sines states:The Law of Cosines, given sides a, b and included angle C, gives the third side c as:The function f(x) = tan x has vertical asymptotes at: