Embibe Experts Solutions for Chapter: Probability, Exercise 1: KCET (UG) 2019

A flashlight has $10$ batteries out of which $4$ are dead. If $3$ batteries are selected without replacement and tested, then the probability that all $3$ are dead is

If $P\left(A\right)=0.59, P\left(B\right)=0.30$ and $P(A\cap B)=0.21$ then $P\left(A^{\text{'}}\cap B^{\text{'}}\right)=$

A bag contains $17$ tickets numbered from $1$ to $17$. A ticket is drawn at random, then another ticket is drawn without replacing the first one. The probability that both the tickets may show even numbers is

Given that $A$ and $B$ are two events such that $P\left(B\right)=\frac{3}{5}, P\left(\frac{A}{B}\right)=\frac{1}{2}$ and $P(A\cup B)=\frac{4}{5}$ then $P\left(A\right)=$

If $A, B$ and $C$ are three independent events such that $P\left(A\right)=P\left(B\right)=P\left(C\right)=P$ then $P$ (at least two of $A, B, C$ occur)$=$

Two dice are thrown. If it is known that the sum of numbers on the dice was less than $6$, the probability of getting a sum as $3$ is

A car manufacturing factory has two plants $X$ and $Y.$Plant $X$ manufactures $70\%$ of cars and plant $Y$ manufactures $30\%$ of cars. $80\%$ of cars at plant $X$ and $90\%$ of cars at plant $Y$ are rated as standard quality. A car is chosen at random and is found to be standard quality. The probability that it has come from plant $X$ is

For the probability distribution given by

The standard deviation $\left(\mathrm{\sigma }\right)$ is