Suppose there is a box containing 7 white balls, 1 black ball, and 2 red balls.

Question

Suppose there is a box containing 7 white balls, 1 black ball, and 2 red balls. Is it possible to add the same number of bais of each color to the box so that when a ball is drawn at random the probabity of the event that t is a black ball is the following? Explian b. 0 24 mmter of balls of each coor to the box so that when a ban s drawn at random the probabily o, a ttack bat being drawn s,Select Preomed chore blew ard.r a. is it possible to add the same necessary, St in the answer box to complete your choice O A. AdingObals of each Color w." cause the prot atality of drawing a black bat to be B. a black ballis It is not possible to add the same number of balts of each color so that the probabiity of drawing

Explanation / Answer

Ans:

a)It is not possible as,adding any number of balls of each colour will not make the proportion of each colour equal.

e.g if we add say 2 balls of each colour to the box,the proportion of ball will be

7+2,1+2,2+2

9,3,4

Probability of drawing black ball=3/(9+3+4)=3/16

it can be 1/3,only when there are equal number of balls of each colour,say 9,9,9

then 9/27=1/3

hence,Adding any number of balls will not make the equal proportion of each color,which is neceassary to be probability of drawing a black ball=1/3

So,Option B is correct.(not possible)

b)if we add 5 balls of each color to the box,then there will be

7+5=12 white balls

1+5=6 black balls

2+5=7 red balls

Now ,probability of drawing a black ball is =6/(12+6+7)=6/25=0.24

Hence,we need to add 5 balls of each color to the box.

So,Option A is correct.

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