Probability practice · Easy

Sixteen players $S_1, S_2, \ldots S_{16}$ play in a tournament. They are divided into eight pairs at random. From each pair a winner is decided on the basis of a game played between the two players of the pair. Assuming that all the palyers are to equal strength. The probability that the players $S_1$ is among the eight winners is

A card is drawn at random from a pack of 100 cards numbered 1 to 100 . The probability of drawing a number, which is a square, is-

Suppose $X$ follows a binomial distribution with parameters $n=6$ and $p$. If $9 P(X=4)=$ $P(X=2)$, then $4 p$ is equal to

An unbiased coin is tossed to get 2 points for turning up a head and one point for the tail. If three unbiased coins are tossed simultaneously, then the probability of getting a total of odd number of points

Out of 15 persons 10 can speak Hindi and 8 can speak English. If two persons are chosen at random, then the probability that one person speaks Hindi only and the other speaks both Hindi and English is

If $X$ is a poisson variate with $P\left( {X = 0} \right) = 0.8,$ then the variance of $X$ is

In a box, there are 20 cards, out of which 10 are labelled as $A$ and the remaining 10 are labelled as $B$. Cards are drawn at random, one after the other and with replacement, till a second $A$ - card is obtained. The probability that the second $A$ - card appears before the third $B$ - card is:

Let $A$ and $B$ be two events associated to a random experiment such that $P$ (Exactly one occurs) $=\frac{2}{5}, P(A \cup B)=\frac{1}{2}$. Then, $P(A \cap B)$ is

6 boys and 6 girls sit in a row randomly. The probability that all 6 girls sit together, is

If $P(A \cap B)=1 / 3, P(A \cup B)=5 / 6$ and $P(A)=1 / 2$, then which one of the following is correct?

Cards are drawn from a pack of 52 playing cards one by one. The probability that exactly 10 cards will be drawn before the first ace is

The probability that in a year of $22 n d$ century chosen at random, there will be 53 Sundays is

A die is thrown 100 times. If getting an even number is considered a success, the variance of the number of successes, is

There are 9999 tickets bearing numbers 0001, 0002, …., 9999. If one ticket is selected from these tickets at random, the probability that the number on the ticket will consists of all different digits, is

Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of getting atmost two heads is:

The probability that a randomly chosen $2 \times 2$ matrix with all the entries from the set of first 10 primes, is singular, is equal to :

If birth to a male child and birth to a female child are equal-probable, then what is the probability that at least one of the three children born to a couple is male?

The probability that an ordinary or a non-leap year has 53 sunday, is

One hundred identical coins, each with probability $p$ or showing up heads are tossed once. If $0 < p < 1$ and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of $p$ is

A bag contains four tickets numbered $00,01,10$ and 11. Four tickets are chosen at random with replacement, then the probability that sum of the numbers on the tickets is 23 , is

$A$ and $B$ are two independent events such that their probabilities are $\frac{3}{{10}}$ and $\frac{2}{{5}}$ respectively. The probability of exactly one of the events happening is

Two contestants play a game as follows: each is asked to select a digit from 1 to 9. If the two digits match they both win a prize. The probability that they will win a prize in a single trial is

Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be a women is

In a box containing 100 bulbs, 10 are defective. What is the probability that out of a sample of 5 bulbs none is defective?

The mean and variance of a binomial distribution are 4 and 3 respectively, then the probability of getting exactly six successes in this distribution is

In a school there are 100 students 60 of them don't like Chocolate and 50 don't like Biscuit and 10 of them like none then how many of them like both?

From a pack of cards two are accidently dropped. Probability that they are of opposite shade is

Three dice are thrown together. The probability that the sum of the numbers appearing on them is 9 , is

An unbiased cubical die is thrown 5 times. The probability that the maximum number appearing on the die is 4 is

A parents has two children. If one of them is boy, then the probability that other is, also a boy, is