Question

there are 18 beads in a box.some of them are white and the remaining are black.the probability of drawing a black bead from it is 1/3 then;
A)how many black bead are there in the box.
B)how many white bead are there in the box.
C)how many white bead should be added to it so that the probability of drawing a black bead becomes 1/4

Answer 1

Hey There!!

We have a total of 18 beads in the box. 

Some of them are white, some are black. 

Suppose the number of black beads = x

We are given that the Probability of drawing a Black Bead is $\frac{1}{3}$  

This means that: 

$\textrm{Probability of drawing black bead }=\frac{x}{18}=\frac{1}{3} \\ \\ \implies x = \frac{18}{3} \\ \\ \textbf{x=6}$

So, There are 6 Black Beads.

This also means that there are (18-6) = 12 White Beads .

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Now, for your third question, we are adding white beads so that probability of drawing a black bead reduces to $\frac{1}{4}$

Suppose we add x white beads 

So, we have


Number of white beads = 12+x
Number of black beads = 6 
Total Number Of beads = 18+x 


Now, we have:

$\textrm{Probability of drawing black bead }=\frac{6}{18+x} = \frac{1}{4} \\ \\ \implies 6\times 4 = 18+x \\ \\ \implies 24-18=x \\ \\ \implies \textbf{x=6}$


Thus, We Must Add 6 White Beads to reduce probability of drawing a black bead to $\frac{1}{4}$


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So, Your answers are: 


A) 6

B) 12

C) 6


Hope it helps
Purva
Brainly Community