Probability

The probability distribution of a random variable $\mathrm{X}$ is Then the standard deviation of $\mathrm{X}$ is

If the range of a random variable $X$ is $\{0,1,2,3,4, \ldots \ldots\}$ with $P(X=k)=\frac{(k+1) a}{3^k}$ for $k \geq 0$, then $a$ is equal to

A box contains 20% defective bulbs. Five bulbs are chosen randomly from this box. The probability that exactly 3 of the chosen bulbs are defective is

A student writes an examination which contains eight true or false questions. If he answers six or more questions correctly, he passes the examination. If the student answers all the questions, then the probability that…

If A and B simultaneously toss one coin each every time, each 50 times, then the probability of not getting tail on both the coins is

Let $\mathrm{A}$ and $\mathrm{B}$ be two independent events of a random experiment. If the probability that both A and B occur is $\frac{1}{6}$ and the probability that neither of them occur is $\frac{1}{3}$, then the…

A basket contains 12 apples in which 3 are rotten. If 3 apples are drawn at random simultaneously from it, then the probability of getting atmost one rotten apple is

Four cards are drawn at random from a pack of 52 playing cards. The probability of getting all four cards of the same suit is

If \(P\) and \(Q\) each toss three coins. The probability that both gets same number of heads, is

Two balls are drawn from an urn containing 7 white, 6 red and 8 black balls one after the other without replacement. Then the probability that atleast one of them is white, is

If $A$ and $B$ throw two dice $100$ times each simultaneously, then the probability that both of them will get even number as the total score at the same time in all the throws is

If $A$ and $B$ are two events of a random experiment such that $P(A)=0.6, P(B)=0.3$ and $P(A \mid B)=0.5$ then $P(\bar{B} \mid \bar{A})=$