Probability practice · Mixed difficulty

In a convex hexagon two diagonals are drawn at random. The probability that the diagonals intersect at an interior point of the hexagon is

A perfect die is thrown twice. The expected value of the product of the number of points obtained in two throws is

A card is selected from a pack of 52 cards.

I. The probability that card is an ace of spades, is $\frac{2}{52}$.

II. The probability that the card is black card, is $\frac{26}{52}$.

The probability that a leap year selected at random contains either 53 Sundays or 53 Mondays, is

Let 0.8 the probability that a man aged 90 years will die in a year. If $p$ is the probability that out of 4 men $A_1, A_2, A_3$ and $A_4$ each aged $90, A_1$ will die in a year and will be the first to die, find $10000 p-2490$ is

A five digit number is chosen at random. The probability that all the digit are distinct and digits at odd places are odd and digits at even place are even, is

Let $A=\{1,3,5,7,9\}$ and $B=\{2,4,6,8\}$. An element $(a, b)$ of their cartesian product $A \times B$ is chosen at random. The probability that $a+b=9$, is

A bag contains 8 red and 7 black balls. Two balls are drawn at random. The probability that both the balls are of the same colour, is

A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade is:

You are given a box with 20 cards in it. 10 of these cards have the letter $I$ printed on them. The other ten have the letter ${T}$ printed on them. If you pick up 3 cards at random and keep them in the same order, the probability of making the word $IIT$ is

If $A$ and $B$ are two given events, then $P(A \cap B)$ is

A coin is tossed 4 times. The probability that atleast one head turn up, is

Two dice are rolled. If the probability of getting different numbers on the these dice is $\frac{p}{q}$ where $p, q$ are relatively prime then $q-p$ is

If $A$ and $B$ are two independent events, then $A$ and $\bar B$ are

Five boys and three girls are seated at random in a row. The probability that no boy sits between two girls is

5 persons $A, B, C, D$ and $E$ are in 9 queue of a shop. The probability that $A$ and $E$ always together is

The probability of the product of 3 numbers chosen from the set $\mathrm{A}=\{1,2,3,4, \ldots \ldots 20\}$ is divisible by 4 is equal to

$A$ and $B$ are two independent events such that $P\left( {A \cup B'} \right) = 0.8$ and $P\left( A \right) = 0.3.$ Then, $P\left( B \right)$ is

One percent of the population suffers from a certain disease. There is blood test for this disease, and it is $99 \%$ accurate, in other words, the probability that it gives the correct answer is 0.99 , regardless of whether the person is sick or healthy. A person takes the blood test, and the result says that he has the disease. The probability that he actually has the disease, is

A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is six. The probability that it is actually a six, is

The probability that a student is not a swimmer is $1 / 5$. The probability that out of 5 students exactly 4 are swimmer is

A bag contains 50 tickets numbered 1, 2, 3, …, 50 of which five are drawn at random and arranged in ascending order of magnitude $\left( {{x_1} < {x_2} < {x_3} < {x_4} < {x_5}} \right).$ The probability that ${x_3} = 30,$ is

A box contains 20 cards of these 10 have letter I printed on them and the remaining 10 have T printed on them. 3 cards are drawn from the box, the probability that we can write IIT with these cards is

Two numbers $a$ and $b$ are selected at random from $1,2, \ldots ., 100$ and are multiplied. The probability that the product $a b$ is divisible by 3 , is

Two dice are rolled one after the other. The probability that the number on the first is smaller than the number on the second is

A die is tossed thrice. If event of getting an even number is a success, then the probability of getting at least two successes is

An elevator starts with $m$ passengers and stops at $n$ floors $(m \leq n)$. The probability that no two passengers alight at the same floor is

Three letters are written to there different persons and addresses on the three envelopes are also written. Without looking at the addresses, the letters are kept in these envelopes. The probability that all the letters are not placed into their right envelopes is

Three six faced dice are tossed together, then the probability that exactly two of the three numbers are equal is

If $A$ and $B$ are independent events and $P\left( C \right) = 0,$ then