Embibe Experts Solutions for Chapter: Solved Mathematics Paper-2, Exercise 1: Exercise

If $P\left(A\cup B\right)=0·83, P\left(A\right)=0·3$ and $P\left(B\right)=0·6$, then the events $A \&\hspace{0.17em}B$ will be

A problem in Mathematics is given to three students $A, B, C$ and their respective probabilities of solving the problem is $\frac{1}{2},\frac{1}{3}$ and $\frac{1}{4}$. Probability that the problem is solved, is

In a hockey match, both teams A and B scored same number of goals up to the end of the game, so to decide the winner, the referee asked both the captains to throw a die alternately and decided that the team, whose captain gets a six first, will be declared the winner. If the captain of team A was asked to start, find their respective probabilities of winning the match and state whether the decision of the referee was fair or not.

Aman and Bhuvan throw a pair of dice alternately. In order to win, they have to get a sum of $8$. Find their respective probabilities of winning if Aman starts the game.

A bag contains $6$ black balls and an unknown number (not greater than $6$) of white balls. Three are drawn successively and not replaced and are all found to be white. Prove that the chance that a black ball will be drawn next is $\frac{477}{909}$.

Find the equation of a plane which bisects the line segment joining the points $A(2, 3, 5)$ and $B(4, 5, 7)$ at right angles. 

_____ is the Father of mental tests

Differentiate between correlation and regression.