Probability practice · Easy

If the mean of a binomial distribution with 9 trials is 6, then its variance is

A box ' $A$ ' contanis 2 white, 3 red and 2 black balls. Another box ' $B$ ' contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box ' $B$ ' is

A bag contains 4 brown and 5 white balls. A man pulls two balls at random without replacement. The probability that the man gets both the balls of the same colour is

If $\frac{1}{4}(1+4 p), \frac{1}{4}(1-p)$ and $\frac{1}{2}(1-2 p)$ are the probabilities of three mutually exclusive events, then $2 p$ is

If $A$ and $B$ are two events. The probability that at most one of $A, B$ occurs, is

The probability of choosing a number divisible by 6 or 8 from among 1 to 90 is

An urn contains 3 red and 5 blue balls. The probability that two balls are drawn in which 2nd ball drawn is blue without replacement, is

A box contains 3 white and 2 red balls. If we draw one ball and without replacing the first ball, the probability of drawing red ball in the second draw is

In a binomial distribution, the mean is 4 and variance is 3. Then, its mode is

The probability of obtaining an even prime number on each die when a pair of dice is rolled is

An urn contains 6 white and 4 black balls. A fair die is rolled and that number of balls are chosen from the urn. The probability that the balls selected are white is

If three integers are chosen at random from the set of first 20 natural numbers, the chance that their product is a multiple of 3 , is

On a Saturday night $20 \%$ of all drives in U.S.A. are under the influence of alcohol. The probability that a driver under the influence of alcohol will have an accident is $0.001.$ The probability that a sober driver will have an accident is $0.0001.$ If a car on a Saturday night smashed into a tree, the probability that the driver was under the influence of alcohol is

In a party 23 persons take their seats at a round table. The odds against two particular persons sitting together are:

A man is known to speak truth in 75% cases. If he throws an unbiased die and tells his friend that it is a six, then the probability that it is actually a six, is

Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals

An article manufactured by a company consists of two parts ${X}$ and ${Y}$. In the process of manufacture of part ${X}$, 9 out of 104 parts may be defective. Similarly, 5 out of 100 are likely to be defective in the manufacture of the part $Y$. The probability that the assembled product will not be defective, is

$A$ and $B$ are two events such that $P(A \cup B)=\frac{3}{4}$, $P(A \cap B)=\frac{1}{4}, P(\bar{A})=\frac{2}{3}$, then $P(\bar{A} \cap B)=$

A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Two cards are drawn at random. The probability that atleast one of them is an ace is

Box-I contains 30 cards numbered 1 to 30 and Box - II contains cards numbered 31 to 50 . A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box - I is

In a binomial distribution $B(n, p)$, the sum and the product of the mean and the variance are 5 and 6 respectively, then $6(n+p-q)$ is equal to

If $X$ follows a binomial distribution with parameters $n = 6$ and $p.$ If $4\left( {P\left( {X = 4} \right)} \right) = P\left( {X = 2} \right),$ then $p =$

The digits $1,2,3,4,5,6,7,8$ and 9 are written in random order to form a nine digit number. The probability that this number is divisible by 4, is

Out of 40 consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is

For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is $\frac{4}{5}$, then the probability that he is unable to solve less than two problem is

In a game two players $A$ and $B$ take turns in throwing a pair of fair dice starting with player $A$ and total of scores on the two dice, in each throw is noted. $A$ wins the game if he throws a total of 6 before $B$ throws a total of 7 and $B$ wins the game if he throws a total of 7 before $A$ throws a total of six. The game stops as soon as either of the players wins. The probability of $A$ winning the game is

A bag contains 4 red and 4 blue balls. Four balls are drawn one by one from the bag, then find the probability that the drawn balls are in alternate colour.

In a book of 500 pages, it is found that there are 250 typing errors. Assume that poisson law holds for the number of errors per page. Then, the probability that a random sample of 2 pages will contain no error, is

Three persons $A, B$ and $C$ are to speak at a function along with 7 other persons. The probability that $A, B$, and $C$ speak together

A box contain $N$ coins, $m$ of which are fair and rest are biased. The probability of getting a head when a fair coin is tossed is $1 / 2$, while it is $2 / 3$ when a biased coin is tossed. A coin is drawn from the box at random and is tossed twice. The first time it shows head and the second time it shows tail. The probability that the coin drawn is fair is