Embibe Experts Solutions for Chapter: Probability, Exercise 2: Exercise-2

Three cards are drawn at random from a pack of well shuffled $52$ cards. Find the probability that one is a king, the other is a queen and the third a jack.

A $2n$ digit number starts with $2$ and all its digits are prime, then the probability that the sum of all $2$ consecutive digits of the number is prime is

There are two urns. There are $m$ white & $n$ black balls in the first urn and $p$ white & $q$ black balls in the second urn. One ball is taken from the first urn & placed into the second. Now, the probability of drawing a white ball from the second urn is

The chance that the top card in the deck is a diamond given that the fourth card from the top is a eight in well shuffled deck.

There is a three volume dictionary among $40$ books arranged on a shelf in random order. Then the reciprocal of probability of these volumes standing in increasing order from left to right (the volumes are not necessarily kept side by side) is

A bag contains undefined coins. It is known that one of these coins shows head on both sides, whereas the other coins are fair. One coin is selected at random and tossed. If the probability that the toss results in head is $\frac{7}{12}$ then find the value of $n$. 

A square matrix of order $3\times 3$ is formed using the elements of the set $\left\{-2016, 0, 2016\right\}$

A variable takes the values of $0, 1, 2, \dots \dots , n$ with frequencies proportional to the binomial coefficients ${}^{n}C_0, {}^{n}C_1, {}^{n}C_2, \dots , {}^{n}C_n,$ then the mean of the distribution is