Probability practice · Mixed difficulty

A dice is rolled 4 times, the numbers appearing are listed. The number of different throws, such that the largest number appearing in the list is 4 , is

In a bag there are three tickets numbered 1, 2, 3. A ticket is drawn at random and put back, and this is done four times. The probability that the sum of the numbers is even, is

$'X'$ speaks truth in $60 \%$ and ' $Y$ ' in $50 \%$ of the cases. The probability that they contradict each other while narrating the some incident, is

An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn; if the drawn ball is red, then a green ball is added to the urn the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is

A box contains 10 mangoes out of which 4 are rotten. 2 mangoes are taken out together. If one of them is found to be good, the probability that the other is also good is

Twelve tickets are numbered from 1 to 12. One ticket is drawn at random, then the probability of the number to be divisible by 2 or 3, is

$2 n$ boys are randomly divided into two subgroups containing $n$ boys each. The probability that the two tallest boys are in different groups is

If the standard deviation of the binomial distribution $(q+p)^{16}$ is 2, then mean of the distribution is

If the mean and variance of a binomial variate $X$ are 2 and 1 respectively, then the probability that $X$ takes a value greater than 1, is

While shuffling a pack of 52 playing cards. Unfortunately 4 cards are dropped on the ground it is known that 2 out of 4 are spades. What is the probability that all dropped 4 are spades?

If 3 numbers are selected from the set $(1,2,3,........., 24)$ without replacement, then what is the probability that the selected numbers do not form an A.P.?

If four positive integers are taken at random and multiplied together, then the probability that the last digit is 1, 3, 7 or 9 is

If $\mathrm{P}(\mathrm{A})=\frac{2}{5}, \mathrm{P}(\mathrm{B})=\frac{3}{10}$ and $\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{5}$, then $\mathrm{P}\left(\mathrm{A}^{\prime} \mid \mathrm{B}^{\prime}\right) \cdot \mathrm{P}\left(\mathrm{B}^{\prime} \mid \mathrm{A}^{\prime}\right)$ is equal to

The probability that the birth days of six different persons will fall in exactly two calendar months is

A three digit number, which is a multiple of 11, is chosen at random. Probability that the number so chosen is also a multiple of 9, is equal to

There are $m$ persons sitting in a row. Two of them are selected at random. The probability that the two selected persons are not together is

An integer is chosen at random from the first 200 positive integers. The probability that the integer chosen is divisible by 6 or 8 is

Let $S$ be the sample space of all five digit numbers. It $p$ is the probability that a randomly selected number from $S$, is multiple of 7 but not divisible by 5 , then $9 p$ is equal to

There are 10 pairs of shoes in a cupboard from which 4 shoes are picked at radndom. The probability that there is at least one pair is

If $n(\mathrm{~A})=1000, n(\mathrm{~B})=500$ and if $n(\mathrm{~A} \cap \mathrm{B}) \geq 1$ and $n(\mathrm{~A} \cup \mathrm{B})=p$, then

A die is thrown. Let $A$ be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then, $P(A \cup B)$ is

A letter is taken at random from the letters of the word 'STATISTICS' and another letter is taken at random from the letters of the word 'ASSISTANT'. The probability that they are the same letter is

$A, B, C$ are three mutually exclusive and exhaustive events associated with a random experiment. If ${P}({B})$ $=\frac{3}{2} {P}({A})$ and ${P}({C})=\frac{1}{2} {P}({B})$, then ${P}({A})=$

Six dice are thrown simultaneously. The probability that exactly three of them show the same face and remaining three show different faces, is

For the married couple living in Jammu, the probability that a husband will vote in an election is 0.5 and the probability that his wife will vote is 0.4 . The probability that the husband votes, given that his wife also votes is 0.7 . Then the probability that husband and wife both will vote is

Three are six verities of a regular hexagon are chosen at random, then the possibility that the triangle with three vertices is equilateral, is equal to

A class consists of 80 students, 25 of them are girls. If 10 of the students are rich and 20 of the students are fair complexioned, then the probability of selecting a fair complexioned rich girl from the class (assuming three traits as independent) is

If $A$ and $B$ each toss three coins. The probability that both get the same number of heads is

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

The probability that when 12 balls are distributed among three boxes, the first will contain three balls is,