JEE Advanced Statistics and Probability — practice questions
89 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Advanced Statistics and Probability in the app →Mean of n numbers x₁, x₂, ..., x_n:Median of sorted data with odd count n:Mode of data set is:Probability of certain event:Total probability of all mutually exclusive outcomes:Standard deviation of n numbers with mean x̄:Variance:For independent events A and B:Mutually exclusive events A and B:Conditional probability:Bayes' theorem:Expected value E(X) of discrete random variable:Bernoulli trial has:Binomial distribution: P(X = k) =Mean of binomial distribution with n trials, success probability p:Variance of binomial:Mean of 10 numbers is 8. If a new value 30 is added, new mean:Box has 5 red, 7 blue balls. Draw 2 without replacement. P(both red):P(both red OR both blue) in 2 draws without replacement from 5R 7B box:A coin tossed 10 times. P(exactly 5 heads):If P(A) = 0.4, P(B) = 0.5, P(A ∩ B) = 0.2: A and B independent?For random variable X uniform on [0, 1]: E(X²) =For uniform U[0,1]: variance =E[X² + Y²] when X, Y are independent identically distributed with E(X) = 0, Var(X) = σ²:Cov(X, X) =Correlation coefficient r:5 cards from deck of 52. P(all spades):Coefficient of variation (CV):Mean of frequency distribution Σf_i x_i / Σf_i. Find mean of: 2(×3), 4(×5), 6(×2): values 2,4,6 with frequenciStandard deviation property: σ(aX + b) =For Poisson distribution with rate λ: P(X = k) =Three-card hand probability of a flush (any same suit):At least one '6' in 4 throws of a fair die:Variance of fair die roll (1-6):P(A) = 1/3, P(B) = 1/2, P(A ∩ B) = 1/6. P(A ∪ B) =From 7 men and 5 women, choose committee of 4 with at least 1 woman:A box has 6 balls, 4 are red. Two balls drawn (without replacement). P(both red):Mean Square Error (MSE) of estimator decomposes as:Properties of normal distribution: ___ % of data within 1 SD of mean.X ~ Binomial(50, 0.4). Find E[X] and Var[X]: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):Chebyshev's inequality: P(|X - μ| ≥ kσ) ≤Two independent X, Y with Var(X) = 4, Var(Y) = 9. Var(X + Y) =Three fair coins are tossed. Let E = "at least two heads" and F = "first coin shows tail". Then P(E|F) isThe conditional probability P(E|F) is defined byThe multiplication rule for probability states P(E ∩ F) equalsTwo events E and F are called independent ifA die is rolled and a coin is tossed simultaneously. If E = "die shows an even number" and F = "coin shows heaBayes' theorem for two disjoint exhaustive hypotheses E₁ and E₂ statesIn a factory, 60% of items come from Machine A and 40% from Machine B. 2% of A-items and 5% of B-items are defA random variable X counts the number of heads in 3 tosses of a fair coin. The mean E(X) isThe variance of the number of heads in 3 fair-coin tosses isFor a Binomial distribution B(n, p), the probability of exactly r successes isA card is drawn at random from a well-shuffled deck of 52. E = "card is a face card" (King, Queen, Jack). P(E)E and F are independent events with P(E) = 0.3 and P(F) = 0.5. Then P(E ∪ F) equalsTwo dice are rolled. Let E = "sum is 8" and F = "at least one die shows 4". Then P(E|F) equalsIf P(A) = 0.4, P(B|A) = 0.5, then P(A ∩ B) equalsFor a random variable X, the variance Var(X) equalsA die is rolled and E is the event of getting a multiple of 7. The event E is best described as:In a random experiment with sample space S, the event S itself always occurs. Such an event is called:An event containing exactly one sample point of the sample space is called:The probability of an event A is 0.7. The probability of its complement, not-A, equals:A fair die is rolled once. The probability of getting an even number is:Two events that cannot occur together in a single trial are called:A coin is tossed three times. The number of outcomes in the sample space is:A fair die is rolled once. The probability that the number shown is a multiple of 3 is:One card is drawn from a well-shuffled pack of 52 cards. The probability that it is an ace is:For two events, P(A) = 0.35, P(B) = 0.45 and P(A and B) = 0.20. Then P(A or B) equals:A and B are mutually exclusive with P(A) = 1/4 and P(B) = 1/3. The probability that A or B occurs is:In set notation, the event 'A occurs but B does not occur' is written as:Events E1, E2, ..., En of a sample space are called exhaustive when:Two dice are thrown together. The total number of outcomes in the sample space is:Under the axiomatic approach, the probability of the sure event S equals:For two events, P(A) = 0.44, P(B) = 0.46 and P(A and B) = 0.16. Then P(A or B) is:With P(A) = 0.44, P(B) = 0.46 and P(A and B) = 0.16, the probability that neither A nor B occurs is:Given P(A or B) = 0.8, P(A) = 0.5 and P(A and B) = 0.2, the value of P(B) is:One card is drawn from a pack of 52. The probability that it is a spade or an ace is:Two dice are thrown. The probability that the sum of the numbers is 8 equals:For any two events A and B, the probability that neither occurs always equals:Two dice are thrown together. The probability of getting a doublet is:One card is drawn from a pack of 52. The probability that it is neither a king nor a queen is:A, B and C are mutually exclusive and exhaustive with P(A) = 1/2 and P(B) = 1/3. Then P(C) equals:A fair coin is tossed three times. The probability of getting at least one head is:A and B are mutually exclusive, P(not A) = 0.65 and P(A or B) = 0.85. Then P(B) equals:One card is drawn from a pack of 52. The probability that it is a red king is:A fair coin is tossed three times. The probability of getting exactly two heads is:Two dice are thrown. The probability that the sum of the numbers is at most 4 is:For two events, P(A) = 0.54, P(B) = 0.69 and P(A and B) = 0.35. The probability that A occurs but B does not i