If a person A speaks the truth in 80% cases and the person B speaks the truth in 75% cases, then the probability that they contradict each other in a statement is

Let E and F are events associated with an experiment. If $P(E) = 0.4$, $P(F) = 0.8$ and $P(F|E) = 0.6$, then $P(E|F)$ is

The random variable X has a probability distribution P(X) of the following form, where k is some number.

$P(X=x) = \begin{cases} k, & \text{if } x=0 \\ 2k, & \text{if } x=1 \\ 3k, & \text{if } x=2 \\ 0, & \text{otherwise} \end{cases}$

Then $P(x \leq 2)$ is :

The probability distribution function of a normal variate with mean $\mu$ and variance $\sigma^2$ is given by:

$f(x) = \frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2}$, $-\infty < x < \infty$, $-\infty < \mu < \infty$, $\sigma > 0$

If $y = f(x)$ be the normal probability curve, then which of the following is correct?

(A) The normal curve is symmetrical about the line $x = \mu$.

(B) Mean, median and mode of the distribution coincide.

(C) Y- axis is an asymptote to the normal curve.

(D) If x increases numerically, $f(x)$ decreases rapidly.

Choose the correct answer from the options given below:

For a biased die, the probabilities of outcomes are given as under.

$P(1)=P(2)=\dfrac{2}{10}, P(3)=P(5)=P(6)=\dfrac{1}{10}, P(4)=\dfrac{3}{10}$.

The die is thrown two times. Let A and B be events defined as

A is getting same number each time and

B is getting a total of 10 or more on die ,

then which one of the following is TRUE?

If A, B and C are three independent events such that P(A)=P(B)=P(C)=x, then P(at least two of A, B, C occur) =

Consider an experiment of tossing 3 coins simultaneously. Define the following events:

$E$ = [Three heads or three tails appear]

$F$ = [At least two heads appear] and

$G$ = [At most two heads appear]

Choose the correct option: