Question

a bag contains 5 red balls and some blue balls.if the probability of drawing a blue ball from the bag is 4 times that of red ball.fimd number of blue ball s.in bag​

Answer 1

Let number of Blue ball be "x".
And no. of Red ball = 5 (given)
So, Total no. of Balls = (5 + x)

Probability of drawing a Blue ball
= x/(5 + x)
Probability of drawing a Red ball
= 5/(5 + x)

Now, according v to question:
The probability of drawing a blue ball from the bag is 4 times that of red ball.

Then, [x/(5 + x)] = 4 × [5/(5 + x)]
cross-multiplying we get,
x × (5 + x) = 4 × 5 × (5 + x)
5x + x² = 100 + 20x
x² - 15x -100 = 0
x² - 20x + 5x -100 = 0
x(x - 20) + 5(x - 20) = 0
(x - 20) (x + 5) = 0
x = 20, -5
now, since x is the number of Blue balls, si it cannot be negative.
So, x = 20
Thus, there are a total number of 20 balls.

Thankyou!!!