Question

A box contains six white balls, eight black balls, and five red balls. How many red balls must be added to the box to the probability of drawing a red ball is 5/6

Answer 1

Answer:

Therefore 65 red balls must be added in the box.

Step-by-step explanation:

Probability:

                   The ratio of the number of the favorable outcomes to the total number of all possible outcomes.

$Probability=\frac{\textrm{Number favorable outcomes}}{\textrm{Total number of outcomes}}$

Given that, A box contains some balls. There are 6 white ball, 8 black ball and 5 red ball in the box.

Let, x number of red red must be added in the box.

Now total number of balls=(6+8+5+x)=19+x

Number of red balls= (5+x)

The probability that a red ball is drawing is

$=\frac{\textrm{Number of red ball}}{\textrm{Number of total ball}}$

$=\frac{5+x}{19+x}$

According to the problem,

$\frac{5+x}{19+x}=\frac56$

$\Rightarrow 6(5+x)=5(19+x)$

⇒30+6x=95 +5x

⇒6x-5x=95-30

⇒x=65

Therefore 65 red balls must be added in the box.