OJEE Probability — practice questions
72 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice OJEE Probability in the app →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 kiEvents $A$ and $B$ are mutually exclusive with $P(A) = 0.4$ and $P(B) = 0.3$. Find $P(A \cup B)$.A bag contains $3$ red, $5$ blue, and $2$ green balls. One ball is drawn at random. What is the probability thA **random variable** is best defined as:A **discrete** random variable is one whose possible values:A **continuous** random variable is one whose values are typically obtained by:For a **probability mass function (p.m.f.)** $f(x_i) = P[X = x_i]$, the two essential conditions are:For a **probability density function (p.d.f.)** $f(x)$ of a continuous random variable over support $S$, the tFor a continuous random variable $X$, the probability that $X$ equals any specific value is:The **cumulative distribution function (c.d.f.)** $F(x)$ of a discrete random variable is:When two fair dice are rolled and $X$ denotes the sum of the upper faces, the range of $X$ is:If a fair coin is tossed twice and $X$ = number of heads, then $P[X = 1]$ equals:The probability that a continuous random variable falls inside an interval $[c, d]$ corresponds to:In the experiment of tossing two fair coins, let $X$ be the number of heads. Then the probability distributionFor the probability distribution $P[X=0]=0.1$, $P[X=1]=k$, $P[X=2]=2k$, $P[X=3]=2k$, $P[X=4]=k$, find $k$.Using the same distribution as above ($P[X=0]=0.1$, $k=0.15$), $P[X < 2]$ equals:If two cards are drawn with replacement from a deck of 52, $P[X = 2]$ where $X$ = number of aces equals:A fair die is thrown. Let $X$ = number of factors of the number on the upper face. $P[X = 2]$ equals:$f(x) = 3x^2$ for $0 < x < 1$ is the p.d.f. of $X$. The probability $P[1/2 < X < 1]$ is:If $f(x) = kx^2(1 - x)$ for $0 < x < 1$ is the p.d.f. of $X$, the value of $k$ is:For p.d.f. $f(x) = x/8$, $0 < x < 4$, the probability $P[x < 1.5]$ is:If $f(x) = 1/5$ for $0 \leq x \leq 5$ (uniform distribution) is the p.d.f. of waiting time for a bus, then theFind $k$ if $f(x) = kx$ for $0 < x < 2$ and 0 otherwise is a valid p.d.f.The c.d.f. $F(x)$ of the p.d.f. $f(x) = 3x^2$ for $0 < x < 1$ is:Three seeds are sown. Each independently germinates with probability 0.5. If $X$ = number that germinate, thenThe probability distribution of the **number of doublets** in three throws of a pair of dice is:Two persons A and B play a game of tossing a coin thrice. If head appears, A gets ₹2 from B; if tail appears, Two cards are drawn with replacement. $X$ = number of aces. The probability $P[X \geq 1]$ equals:For p.d.f. $f(x) = x^2/3$ for $-1 < x < 2$, the probability $P[0 < X \leq 1]$ equals:If $f(x) = x/2$ for $-2 < x < 2$ (and 0 elsewhere), is it a valid p.d.f.?$f(x) = e^{-x}$ for $0 < x < \infty$ (and 0 elsewhere) is the p.d.f. of an **exponential** random variable. ThFor p.d.f. $f(x) = k(4 - x^2)$ for $-2 \leq x \leq 2$ (and 0 elsewhere), the value of $k$ is:For the c.d.f. $F(x) = 3x - 2x^3$ (from p.d.f. $f(x) = 3(1 - 2x^2)$ on $[0, 1]$), $F(0.5)$ equals:If a fair coin is tossed $n$ times, the probability of any exact pattern (like all heads) is:If a die is thrown and 'getting an odd number' is success, then $p$ and $q$ are:A bag has balls marked 0–9. Four balls drawn with replacement. Probability that **none** is marked '0' is:A multiple-choice exam has 5 questions, each with 3 options. Probability that a student gets at least 4 correcProbability of bomb hitting target = 0.8. Out of 10 bombs dropped, probability that **exactly 2 miss** equals A multiple-choice exam has 10 questions each with 5 options. The probability that a student getting **8 or morThe 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:For mutually exclusive events A and B, P(A or B) equals:Find mean of {2, 4, 6, 8, 10}:Mode of {1, 2, 2, 3, 4, 4, 4, 5}:Variance of {2, 4, 6, 8, 10}:Standard deviation of {2, 4, 6, 8, 10}:P(at least one head in 2 fair coin tosses):Probability of drawing a heart from a standard 52-card deck:P(drawing an Ace OR King from a deck) =Two dice rolled. P(sum = 7) =Bayes' theorem relates P(A|B) and P(B|A):Number of ways to arrange 5 distinct books on a shelf:Number of ways to choose 3 students from a class of 10:A box has 5 red, 3 blue marbles. Probability of drawing 2 red and 1 blue in any order (without replacement, 3 For a Poisson distribution with mean λ = 3, P(X = 2):Standard deviation has the same units as:For 50 students with mean score 60 and variance 25, the coefficient of variation (sigma/mean × 100%):P(picking a king OR a heart from 52 cards):Two events A and B: P(A) = 0.3, P(B) = 0.4, P(A and B) = 0.1. Are they independent?5 cards drawn from a standard deck. Probability all 5 are aces:Number of distinguishable arrangements of letters in 'STATISTICS':Conditional probability P(A | B) is defined as:In a survey, 60% read newspaper A, 40% read B, 20% read both. P(reading neither):Binomial distribution: P(X = k) for n trials, success probability p:E(X) and Var(X) for fair coin tossed n times (success = heads, p = 0.5):Two cards drawn from a deck (no replacement). P(both kings):