Embibe Experts Solutions for Chapter: Probability, Exercise 1: Exercise 1

A bag contains $20$ coins. If the probability that the bag contains exactly $4$ biased coin is $\frac{1}{3}$ and that of exactly $5$ biased coin is $\frac{2}{3}$, then the probability that all the biased coin are sorted out from the bag in exactly $10$ draws is

Before a race the chance of three runners $A, B$ & $C$ were estimated to be proportional to $5, 3 \& 2$ respectively but during the race $A$ meets with an accident which reduces his chance to $\frac{1}{3}$. If the respective chances of $B$ and $C$ are $P\left(B\right)$ and $P\left(C\right)$ then -

For any two events $A \& B$ in a sample space :

If $A \& B$ are two events such that $P\left(B\right)\ne 1, B^C$ denotes the event complementary to $B$, then -

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

In a knockout tournament $2^n$ equally skilled players; $S_1, S_2........S_{2^n}$ are participating. In each round players are divide in pair at random and winner from each pair moves in the next round. If $S_2$ reaches the semifinal then the probability that $S_1$ wins the tournament is $\frac{1}{20}$. Find the value of '$n$'.

All the face cards from a pack of $52$ playing cards are removed. From the remaining pack half of the cards are randomly removed without looking at them and then randomly drawn two cards simultaneously from the remaining. If the probability that, two cards drawn are both aces, is $\frac{p\left({}^{38}C_{20}\right)}{{}^{40}C_{20}.{}^{20}C_2}$, then find the value of $p$.

There are $2$ groups of subjects one of which consist of $5$ science subjects & $3$ Engineering subjects & other consists of $3$ science & $5$Engineering subjects. An unbiased die is cast. If the number $3$ or $5$ turns up a subject is selected at random from first group, otherwise the subject is selected from $2^{\mathrm{nd}}$ group. Find the probability that an Engineering subject is selected is $\frac{x}{24}$, then $x$ is