Question

a bag contain 6 white ball and some Black balls if the propability of getting a black Ball is 2/3 times the probability of getting a white ball then the the number of black Ball in the bag is​

Answer 1

N Number of black balls will be nine and a number of white balls is six

Answer 2

The number of black balls in the bag = 4

Given :

A bag contain 6 white ball and some black balls if the propability of getting a black Ball is 2/3 times the probability of getting a white ball

To find :

The number of black balls in the bag

Solution :

Step 1 of 2 :

Form the equation to calculate number of black balls in the bag

Let number of black balls in the bag = x

Number of white balls in the bag = 6

So total number of balls in the bag = (6 + x)

Probability of getting white ball = 6/(6 + x)

Probability of getting black ball = x/(6 + x)

By the given condition

$\displaystyle \sf \frac{x}{(6 + x)} = \frac{2}{3} \times \frac{6}{(6 + x)}$

Step 2 of 2 :

Calculate number of black balls in the bag

$\displaystyle \sf \frac{x}{(6 + x)} = \frac{2}{3} \times \frac{6}{(6 + x)}$

$\displaystyle \sf{ \implies }\frac{x}{(6 + x)} = \frac{4}{(6 + x)}$

$\displaystyle \sf{ \implies }x = 4\: \: \: \bigg[ \: \because \:(6 + x) \ne 0 \bigg]$

Hence number of black balls in the bag = 4

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