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

If the letters of the word $\text{'}\mathrm{REGULATION}\text{'}$ be arranged at random, the probability that there will be exactly $4$ letters between $R$ and $E$ 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

$A$ speaks truth in $60\%$ cases and $B$ speaks truth in $70\%$ cases. The probability that they will say the same thing while describing single event, is

In a Binomial distribution, the mean is three times its variance. What is the probability of exactly $3$ successes out of $5$ trials ?