Probability practice · Mixed difficulty

A bag contains 10 white and 3 black balls. Balls are drawn one-by-one without replacement till all the black balls are drawn. The probability that the procedure of drawing balls will come to an end at the seventh draw 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

A bag contains 5 white, 3 black balls. 2 balls are drawn one by one, their colour noted and
replaced in bag then probability that one ball is white and one is black, 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

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

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 fair coin is tossed a fixed number of times. If the probability of getting exactly 3 heads equals the probability of getting exactly 5 heads, then probability of getting exactly one head is

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

A fair coin is tossed 2019 times. Probability of getting at least 1010 heads is

The odds in favour of standing first of three student appearing in an enamination are $1: 2,2: 5$ and $1: 7$ respectively. The probability that either of them will stand first, 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

A locker can be opened by dialing a fixed three-digit code (between 000 and 999). A stranger, who does not know the code, tries to open the locker by dialing three digits at random. If $p$ is the probability that the stranger succeeds at the $k$ th trial, then $1000 p$ is equal to. (Assume that the stranger does not repeat unsuccessful combinations.)

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

A JEE aspirant estimates that he will be successful with an 80% chance if he studies 10 hr/day with 60%
chance if he studies 7 hr/day and with 40% chance if he studies 4 hr/day. Further, he believes that he will
study 10 hr, 7 hr and 4 hr/day with probability 0.1, 0.2 and 0.7 respectively. Given that he is successful,
the probability that he studies for 4 hr/day equals.

Let $A$ and $B$ two events such that $P\left( {\overline {A \cup B} } \right) = \frac{1}{6},P\left( {A \cap B} \right) = \frac{1}{4}$ and $P\left( {\bar A} \right) = \frac{1}{4},$ where $\bar A$ stands for complement of event $A$. Then, events $A$ and $B$ are

In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to

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

A man draws a card from a pack of 52 cards and then replaces it. After shuffling the pack, he again draws a card. This he repeats a number of times. The probability that he will draw a heart for the first time in the third draw is

$A$ is a set containing n elements. A subset $P$ of $A$ is chosen at random. The set $A$ is reconstructed by replacing the elements of $P$. A subset $Q$ is again chosen at random. The probability that $P=Q$, is

If $X$ is a binomial variate with the range {0,1,2,3,4,5,6} and $P\left( {X = 2} \right) = 4P\left( {X = 4} \right),$ then the parameter $p$ of $X$ is

A letter is taken out at random from `ASSISTANT’ and another is taken out from `STATISTICS’. The probability that they are the same letters is

A letter is known to have come from CHENNAI, JAIPUR, NAINITAL, DUBAI and MUMBAI. On the post mark only two consecutive letters AI are legible. Then the probability that it come from MUMBAI, is

Five coins are tossed simultaneously. The probability that at least one head turning up, is