List of top Engineering Mathematics Questions on Probability asked in TS PGECET

If a die is rolled twice, what is the probability that the sum of the numbers is 7?

In a communication network, 98% of messages are transmitted correctly with no error. If the random variable X denotes the number of messages transmitted with error, then the probability that at most two messages are transmitted with error out of 1000 messages sent, is

Two numbers are drawn simultaneously from the set of integers from 1 to 12. If it is known that the sum of drawn two numbers is odd, then the probability that only one of the two numbers is a prime number, is

Let $X$ follow Binomial distribution with parameters $12$ and $p$, let $q = 1 - p$. If \[ \sum_{x=0}^{12}(x - 12p)^2 \cdot {}^{12}C_x \cdot q^{12 - x} \cdot p^x = \frac{8}{3} \quad \text{and} \quad P(X>10) = \left(\frac{2}{3}\right)^K, \, (K>1), \] then $K =$

If \( X \) is a continuous random variable whose probability density function is given by \[ f(x) = \begin{cases} k(4x - 2x^2), & 0<x<2 \\ 0, & \text{otherwise} \end{cases} \quad \text{then the value of } k \text{ is:} \]

The probability of getting a total of 5 at least once in three tosses of a pair of fair dice is:

If the mean of a random variable which follows exponential distribution is \( \frac{1}{3} \), then the probability that the random variable \( X \) takes the values more than \( r \) is greater than \( \frac{1}{e^5} \), then

If $ X $ is a Poisson variate such that $ P(X=1) = \frac{3}{10} $ and $ P(X=2) = \frac{1}{5} $, then the mean of the distribution is:

Let a continuous random variable $X$ follow Normal distribution with mean $\mu$ and variance $\sigma^2$. Let $Z = \dfrac{X - \mu}{\sigma}$. If $P(Z>Z_1) = 0.12$ and $P(Z>Z_2) = 0.76$, then $P(Z_2<Z<Z_1) =$

The standard deviation of a Poisson distribution is $\sigma$. If $P(X = r) = K$, then $P(X = r + 2) =$

A, B, C are three mutually disjoint exhaustive events with $P(A) \neq 0$, $P(B) \neq 0$, $P(C) \neq 0$. $E$ is any arbitrary event. If $P(A) = \dfrac{4}{9}$, $P(B) = \dfrac{2}{9}$, $P(E|A) = \dfrac{3}{10}$,
$P(E|B) = \dfrac{5}{10}$, $P(E|C) = \dfrac{8}{10}$, and $P(E) = \dfrac{12}{23}$, then $P(C) =$

If $ x=\alpha, y=\beta, z=\gamma $ is a positive integral solution of the equation $ x+y+z=12 $, the probability that it is such that $ \alpha<\beta<\gamma $ is

Three students A, B and C write an entrance exam. The chance that at least one of them passes the exam is \( \frac{3}{4} \). If the probability that A and C pass the exam are respectively \( \frac{1}{2} \) and \( \frac{1}{4} \), then the probability that B does not pass that exam is: