If the roots of each of the equations 2x^2+x- | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For the equation $2x^2+x-1=0$,we have $2x^2+2x-x-1=0 \Rightarrow 2x(x+1)-1(x+1)=0$,so $x = \frac{1}{2}, -1$. Since probability $P \in [0, 1]$,we t

Vedclass · Accepted Answer

exhaustive

Vedclass · Answer

(B) For the equation $2x^2+x-1=0$,we have $2x^2+2x-x-1=0 \Rightarrow 2x(x+1)-1(x+1)=0$,so $x = \frac{1}{2}, -1$. Since probability $P \in [0, 1]$,we take $P_1 = \frac{1}{2}$.For the equation $3x^2-10x+3=0$,we have $3x^2-9x-x+3=0 \Rightarrow 3x(x-3)-1(x-3)=0$,so $x = \frac{1}{3}, 3$. Since probability $P \in [0, 1]$,we take $P_2 = \frac{1}{3}$.For the equation $6x^2+11x-2=0$,we have $6x^2+12x-x-2=0 \Rightarrow 6x(x+2)-1(x+2)=0$,so $x = \frac{1}{6}, -2$. Since probability $P \in [0, 1]$,we take $P_3 = \frac{1}{6}$.Sum of probabilities $P_1 + P_2 + P_3 = \frac{1}{2} + \frac{1}{3} + \frac{1}{6} = \frac{3+2+1}{6} = 1$.Since the sum of the probabilities of the events is $1$,the events are exhaustive.

If the roots of each of the equations $2x^2+x-1=0$,$3x^2-10x+3=0$,and $6x^2+11x-2=0$ correspond to probabilities of three events of a random experiment,then those events are

Similar Questions

$A$ problem in mathematics is given to $4$ students whose chances of solving it individually are $\frac{1}{2}, \frac{1}{3}, \frac{1}{4},$ and $\frac{1}{5}.$ The probability that the problem will be solved by at least one student is

Four dice (six-faced) are rolled. The number of possible outcomes in which at least one die shows $2$ is

Let $X$ be a set containing $n$ elements. If two subsets $A$ and $B$ of $X$ are picked at random,the probability that $A$ and $B$ have the same number of elements is:

$A$ and $B$ toss a coin alternatively,the first to show a head being the winner. If $A$ starts the game,the chance of his winning is

The probability of obtaining an even prime number on each die,when a pair of dice is rolled,is . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module