Probability

If a random variable X follows the Binomial distribution B (33, p) such that 3P (X = 0) = P (X = 1) then the value of $\frac{P\left(X=15\right)}{P\left(X=18\right)}-\frac{P\left(X=16\right)}{P\left(X=17\right)}$ is equal to :L

Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2 balls drawn from it at random are found to be 1 red and 1 black. If the probability that both balls come from Bag A is $\frac{6}{11},$ then n is equal to ________.

In an examination, there are 1- true-false type questions. Out of 10, at student can guess the answer of 4 questions correctly with probability $\frac{3}{4}$ and the remaining 6 questions correctly with probability $\frac{1}{4}$ . If the probability that the student guesses the answer of exactly 8 questions correctly out of 10 is $\frac{27k}{4^{10}},$then k is equal to

A random variable X has the following probability distribution

The maximum number of compound propositions, out of   $p\vee r\vee s,p\vee r\vee \sim s,p\vee \sim q\vee s,\sim p\vee \sim r\vee s,\sim p\vee \sim r\vee \sim s,\sim p\vee q\vee \sim s,$ $q\vee r\vee \sim s,q\vee \sim r\vee \sim s,\sim p\vee \sim q\vee \sim s$ that can be made simultaneously true by an assignment of the truth values to p, q, r and s, is equal to………….

If vertex of a parabola is (2, -1) and the equation of its directrix is 4x – 3y = 21, then the length of its latus rectum is:

Let the plane 2x + 3y + z + 20 = 0 be rotated through a right angle about its line of intersection with the plane x – 3y + 5z = 8. If the mirror image of the point $\left(2,-\frac{1}{2},2\right)$ in the rotated plane in B(a, b, c), then

If the probability that a randomly chose 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is p, then 96 p is equal to……….

If the lines $\overrightarrow{r}=\left(\widehat{i}-\widehat{j}+\widehat{k}\right)+\lambda \left(3\widehat{j}-\widehat{k}\right)$ $\stackrel{}{}\stackrel{}{}\stackrel{}{}\stackrel{}{}\stackrel{}{}\stackrel{}{}$ and $\overrightarrow{r}=\left(\alpha \widehat{i}-\widehat{j}\right)+\mu \left(2\widehat{i}-3\widehat{k}\right)$ $\stackrel{}{}\stackrel{}{}\stackrel{}{}\stackrel{}{}\stackrel{}{}$ are coplanar, then the distance of the plane containing these two lines from the point (, 0, 0) is:

The probability of a man hitting a target is $\frac{1}{10}$ . The least number of shots required, so that the probability of his hitting the target at least once is greater than $\frac{1}{4}$ , is(Probability)