Probability practice · Easy

A man is known to speak truth 3 out of 4
times. He takes out a card at random from a well shuffled
pack of 52 playing cards, and reports it is a king. The
probability that its actually a king is

A book contains 1000 pages. A page is chosen at random. The probability that the sum of the digits of the marked number on the page is equal to 9 , is

There are 4 envelopes corresponding to 4 letters. If the letters are placed in the envelopes at random. The probability that all the letters are not placed in the right envelopes, is

If $\overline{{E}}$ and $\overline{{F}}$ are the complementary events of events ${E}$ and ${F}$ respectively and if $0 < {P}({F}) < 1$, then

A bag contain 5 black balls, 4 white balls and 3 red balls. If a ball is selected randomly, the probability that it is a black or red ball, is

Six faces of an unbiased die are numbered with 2, 3, 5, 7, 11 and 13. If two such dice are thrown, then the probability that the sum on the uppermost faces of the dice is an odd number, is

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

If events are independent and $P\left( A \right) = \frac{1}{3},\;P\left( B \right) = \frac{1}{3},\;P\left( C \right) = \frac{1}{4},\;$ then $\mathrm{P}\left( {A' \cap B' \cap C'} \right)$ is equal to

One Indian and four American men and their wives are to be seated randomly around a circular table. The conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife, is

If two squares are chosen at random on a chess board, the probability that they have a side in common is

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

$A$ and $B$ toss a coin alternatively till one of them gets a head and wins the game. If $A$ begins the game, the probability $B$ wins the game is

If the probability for $A$ to fail in an examination is 0.2 and that for $B$ is 0.3, then the probability that either $A$ or $B$ fails, is

Two numbers a and b are chosen at random from the set of first 30 natural numbers. The probability that ${a^2} - {b^2}$ is divisible by 3 is

The records of a hospital show that 10% of the cases of a certain disease are fatal. If 6 patients are suffering from the disease, then the probability that only three will die, is

A fair coin is tossed a fixed number of times. If the probability of getting 4 heads equals the probability of getting 7 heads, then the probability of getting 2 heads is

A die is loaded so that the probability of face $i$ is proportional to $i, i=1,2, \ldots, 6$. The probability of an even number occuring when the die is rolled, is

$A$ is the set of all four digit natural numbers which has exactly one digit ' 7 '. A number is chosen at random from the set $A$. The probability that the chosen number when divided by 5 leaves the remainder 2 , is

The letters of the word 'ARTICLE' are arranged at random. The Probability that the vowels may occupy the even places, is

Two numbers $x$ and $y$ are chosen at random from the set $\{1,2,3, \ldots, 30\}$. The probability that $x^2-y^2$ is divisible by 3 is

Suppose an unbiased die has $n$ sides numbered $i=1,2$, .... $n$. The die is tossed $n$ times (assume independence) and a "match" is defined to be the occurrence of side $i$ on the its roll. The probability of at least one match is

What is the probability that when one die is thrown, the number appearing on top is even?

A fair die is rolled repeatedly. The probability that 1 occurs for the first time at the even throw is

The probability of choosing randomly a number $c$ from the set {1, 2, 3, ….., 9} such that the quadratic equation ${x^2} + 4x + c = 0$ has real roots is

A die is thrown 5 times. Getting an odd number is consider a success. The variance of the distribution is

If $4P\left( A \right) = 6P\left( B \right) = 10P\left( {A \cap B} \right) = 1,$ then $P\left( {\frac{B}{A}} \right)$ is equal to

Three six-faced dice are thrown together. The probability that the sum of the numbers appearing on the dice is $k(9 \leq k \leq 14)$ is

A dice is thrown two times. If getting the odd number is considered as success, then the probability of two successes is

A man takes a step forward with probability 0.4 and back-ward with probability 0.6. The probability that at the end of eleven steps he is one step away from the starting point is

In $x = {33^n},n$ is a positive integral value, then what is the probability that $x$ will have 3 at its units place?