Probability · Mathematics · TS EAMCET

The numbers $2,3,5,7,11,13$ are written on six distinct paper chits. If 3 of them are chosen at random, then the probability that the sum of the numbers on the obtained chits is divisible by 3 , is

If two dice are rolled, then the probability of getting a multiple of 3 as the sum of the numbers appeared on the top faces of the dice, if it is known that their sum is an odd number, is

If a random variable $X$ has the following probability distribution, then its variance is

X = x	1	3	5	2
P(X = x)	$3 K^2$	K	$K^2$	2K

The mean and variance of a binomial variate $X$ are $\frac{16}{5}$ and $\frac{48}{25}$ respectively. IfP $(X > 1)=1-K\left(\frac{3}{5}\right)^{7}$, then $5 K=$

If three numbers are randomly selected from the set $\{1,2,3, \ldots \ldots 50\}$, then the probability that they are in arithmetic progression is

The probability that exactly 3 heads appear in six tosses of an unbiased coin, given that first three tosses resulted in 2 or more heads is

A student has to write the words ABILITY, PROBABILITY, FACILITY, MOBILITY. He wrote one word and erased all the letters in it except two consecutive letters. If 'LI' is left after erasing then the probability that the boy wrote the word PROBABILITY is

Two cards are drawn at random one after the other with replacement from a pack of playing cards. If $X$ is the random variable denoting the number of ace cards drawn, then the mean of the probability distribution of X is

If two dice are thrown, then the probability of getting co-prime numbers on the dice is

If two cards are drawn at random simultaneously from a well shuffled pack of 52 playing cards, then the probability of getting a cards having a composite number and a card having a number which is a multiple of 3 is

Bag $P$ contains 3 white, 2 red, 5 blue balls and bag $Q$ contains 2 white, 3 red, 5 blue balls. A ball is chosen at random from $P$ and is placed in $Q$. If a ball is chosen from bag $Q$ at random, then the probability that it is a red ball is

If the probability distribution of a random variable $X$ is as follow, then the variance of $X$ is

$X=x$	2	3	5	9
$P(X=x)$	$k$	$2 k$	$3 k^2$	$k$

Among the 5 married couples, if the names of 5 men are matched with the names of their wives randomly, then the probability that no man is matched with name of his wife is

If 3 dice are thrown, the probability of getting 10 as the sum of the three numbers that appeared on the top faces of the dice is

Three similar urns $A, B, C$ contain 2 red and 3 white balls; 3 red and 2 white balls; 1 red and 4 white balls respectively. If a ball selected at random from one of the urns is found to be red, then the probability that it is drawn from urn $C$ is

If a random variable X has the following probability distribution, then the mean of $X$ is $$ \begin{array}{c|c|c|c|c} X=x_1 & 1 & 2 & 3 & 5 \\ \hline p\left(X=x_i\right) & 2 k^2 & k & k & k^2 \end{array} $$

A A fair coin is tossed a fixed number of times. If the probability of getting 5 heads is equal to the probability of getting 4 heads, then the probability of getting 6 heads is

When 2 dice are thrown, it is observed that the sum of the numbers appeared on the top faces of both the dice is a prime number. Then, the probability of having a multiple of 3 among the pair of numbers thus obtained is

If 2 cards are drawn at random from a well shuffled pack of 52 playing cards from the same suit, then the probability of getting a face card and a card having a prime number is

A dealer gets refrigerators from 3 different manufacturing companies $C_1, C_2$ and $C_3 .25 \%$ of his stock is from $C_1, 35 \%$ from $C_2$ and $40 \%$ from $C_3$. The percentages of receiving defective refrigerators from $C_1, C_2$ and $C_3$ are $3 \% 2 \%, 1 \%$ respectively. If a refrigerator sold at random is found to be defective by a customer, then the probability that it is from $\mathrm{C}_2$ is

If the probability that a student selected at random from a particular college is good at mathematics is 0.6 , then the probability of having two students who are good at Mathematics in a group of 8 students of that college standing in front of the college, is

If on an average 4 customers visit a shop in an hour, then the probability that more than 2 customers visit the shop in a specific hour is