MHT-CET Probability — practice questions
36 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice MHT-CET Probability in the app →A **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 mor