Question

a bag containing X red balls and 5 green balls. 2 balls are picked up randomly one after other without replacement from the bag then the probability of both balls being red is 3/7. what will be the value of x

Answer 1

Answer:

The value of x is 10

Step-by-step explanation:

As per given data,

Total number of balls = x+5

Given:

$\text{The probability of getting 2 red balls =}\frac{3}{7}$

$\implies\:\frac{x}{x+5}*\frac{(x-1)}{x+4}=\frac{3}{7}$

$\implies\:\frac{x(x-1)}{(x+5)(x+4)}=\frac{3}{7}$

$\implies\:\frac{x^2-x}{(x^2+9x+20}=\frac{3}{7}$

$\implies\:7(x^2-x)=3(x^2+9x+20)$

$\implies\:7x^2-7x=3x^2+27x+60$

$\implies\:4x^2-34x-60=0$

$\implies\:4x^2-40x+6x-60=0$

$\implies\:4x(x-10)+6(x-10)=0$

$\implies\:(4x+6)(x-10)=0$

$\implies\:(2x+3)(x-10)=0$

$\implies\:x=\frac{-3}{2},10$

But x cannot be negative

The value of x is 10