Probability practice · Medium

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 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

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.)

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

$A$ 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

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

If there are 6 girls and 5 boys who sit in a row, then the probability that no two boys sit together is

A random variable $X$ follows binomial distribution with mean $\alpha$ and variance $\beta$. Then

A box contains 2 fifty paise coins, 5 twenty five paise coins and 15 ten paise coins. Five coins are taken out of the box at random. Probability that the value of these five coins is less than one rupee and fifity paise is

The probability that a rectangle picked up from a chessboard has the area $6 \mathrm{~cm}^2$ where the distance between consecutive parallel lines on the board is $1 \mathrm{~cm}$, is

If in a trial the probability of success is twice the probability of failure. In six trials the probability of at least four successes is

If three numbers are selected from the set of the first 20 natural numbers, the probability that they are in $G P$, is

From a pack of 52 playing cards, half of the cards are randomly removed without looking at them. From the remaining cards, 3 cards are drawn randomly. The probability that all are king, is :

The probability that $A$ speaks truth is $\frac{4}{5}\mathrm{\;}$ while this probability for $B$ is $\frac{3}{4}$. The probability that they contradict each other when asked to speak on a fact, is

A fair die is thrown twenty times. The probability that on the tenth throw the fourth six appears, is

When a missile is fired from a ship, the probability that it is intercepted is $\frac{1}{3}$ and the probability that the missile hits the target, given that it is not intercepted, is $\frac{3}{4}$. If three missiles are fired independently from the ship, then the probability that all three hit the target, is

India play two matches each with West Indies and Australia. In any match the probabilities of India getting points 0,1 and 2 are $0.45,0.05$ and $0.50$, respectively. Assuming that the outcomes are independent, then the probability of India getting atleast 7 points, is

A die is rolled three times, if $p$ be the probability of getting a large number than the previous number, then the value of $54 p$ is

If the probability that the random variable $X$ takes values $x$ is given by $P(X=x)=k(x+1) 3^{-x}$, $x=0,1,2,3, \ldots$. , where $k$ is a constant, then $P(X \geq 2)$ is equal to

The probability of India winning a test match against West-Indies is $\frac{1}{2}$ assuming independence from match to match the probability that in a match series India’s second win occurs at the third test, is

Four dice are rolled. The probability that the same number will appear on each of them is .

Past records reveal that during a particular was, out of 9 vessels expected to arrive at the Mumbai harbour exactly 7 reached the harbour safely. If 3 vessels were expected to arrive there on a particular data, the probability that exactly two would arrive at the harbour safely, is

These are four balls of different colours and four boxes of colours, same as those of the balls. The number of ways in which the balls, one each in a box, could be placed such that a ball does not go to a box of its own colour is

Two cards are drawn from a pack of 52 cards. What is the probability that at least one of the cards drawn is an ace

In a test, an examines either guesses or copies or knows the answer to a multiple choice questions with four choices. The probability that he makes a guess is $\frac{1}{3}$ and the probability that he copies the answer is $\frac{1}{6}.$ The probability that his answer is correct given that he copies it is $\frac{1}{8}.$ The probability that his answer is correct, given that he guesses it is $\frac{1}{4}.$ The probability that they knew the answer to the questions given that he correctly answered is

Two number $a, b$ are chosen from the set of integers $1,2,3, \ldots ., 39$, then probability that the equation $7 a-9 b=0$ is satisfied, is

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