Question

That contains 5 red balls and some blue balls if the probability of drawing a blue what is double that of a red ball determine the number of blue balls in the bag.

Answer 1

LET THE BLUE BALL BE=X

TOTAL NO. OF BALLS = NO. OF BLUE BALLS + NO. OF RED BALLS

= X + 5

PROBABILITY OF GETTING BLUE BALL = X / X + 5

PROBABILITY OF GETTING RED BALL = 5/ X +5

ACCORDING TO THE QUESTION,

X / X + 5 = 2 * 5 / X + 5

CANCELLING X+5 FROM BOTH TERMS AS THEY ARE COMMON

X = 10

SO, THERE ARE 10 BLUE BALLS IN THE BAG

Answer 2

Solution :

Let there be x blue balls in the bag.

∴ Total number of balls in the bag = 5 + x

Now,

          $p_{1}$ = Probability of drawning a blue ball = $\frac{x}{5 + x}$

          $p_{2}$ = Probability of drawing a red ball = $\frac{5}{5 + x}$

But it is given that $p_{1}$ = $2p_{2}$

⇒ $\frac{x}{5 + x}$ = $2 \times \frac{5}{5 + x}$

⇒ x = 10