Probability practice · Mixed difficulty

Three different numbers are selected at random from the set $A=\{1,2,3, \ldots, 10\}$. The probability that the product of two of the numbers is equal to third, is

If $A$ and $B$ are mutually exclusive events with $P\left( A \right) = \frac{1}{2} \times P\left( B \right)$ and $A \cup B = S,$ (total sample space) then $P\left( A \right)$ is equal to

$A$ and $B$ are the independent events. The probability that both occur simultaneously is $\frac{1}{6}$ and the probability that neither occur is $\frac{1}{3}$. The probability of occurrence of the events $A$ and $B$ is

The probability that a randomly chosen 5-digit number is made from exactly two digits is

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

From first 100 natural numbers, 3 numbers are selected. If these numbers are in A.P., then the probability that these numbers are even 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

If $A$ and $B$ are two events such that $P\left( A \right) > 0$ and $P\left( B \right) \ne 1,$ then $P(\bar A|\bar B)$ is equal to

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?

Two numbers are selected at random from the numbers $1,2, \cdots, n$. Let $p$ denote the probability that the difference between the first and second is not less than $m$ (where $0 < m< n$ ). If $n=25$ and $m=10$ then $5 p$ is equal

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

A number $x$ is chosen at random from the set $\{1,2,3,4, \ldots$, $100\}$. Define the event: $\mathrm{A}=$ the chosen number $\mathrm{x}$ satisfies $\frac{(\mathrm{x}-10)(\mathrm{x}-50)}{(\mathrm{x}-30)} \geq 0$
Then P (A) 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