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

If an integer $q$ is chosen at random in the interval $-10\le q\le 10,$ then the probability that the roots of the equation $x^2+qx+\left(\frac{3q}{4}+1\right)=0$ are real is

A dice is thrown twice and the sum of the numbers appearing is observed to be $8$. The conditional probability that the number $5$ has appeared at least once is

$A \& B$ having equal skill, are playing a game of best of $5$ points. After $A$ has won two points and $B$ has won one point, the probability that $A$ will win the game is:

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

A six faced die is so biased that it is thrice likely to show an even number than an odd number, when thrown. If the die is thrown twice, the probability that sum of the numbers on the die is even, is

From a pack of cards, two cards are drawn one- by- one. Then, the probability that first card is an ace while the second card is honoured (before drawing the second card, the first card is not replaced in the pack of cards) will be

If $A$ and $B$ are two events such that $2P\left(A\right)=3P\left(B\right),$ where $0<P\left(A\right)<P\left(B\right)<1,$ then which one of the following is correct?

A dice is weighted so that the probability of different faces to turn up is as given

If $P\left(\frac{A}{B}\right)=p_1$ and $P\left(\frac{B}{C}\right)=p_2$ and $P\left(\frac{C}{A}\right)=p_3$, then the values of $p_1, p_2, p_3$, respectively are Take the events $A, B \& C$ as $A=\left\{1,2,3\right\}, B=\left\{2,3,5\right\}$ and $C=\left\{2,4,6\right\}$.