Question

A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x.

Solution

Number of black balls in the box = x
Total number of balls in the box = 12

i.e., n(S) = 12

(0 Let A be the favourable outcomes of getting black ball, then
n(A) = x
Therefore,
P(A) = $fraction numerator n left parenthesis A right parenthesis over denominator n left parenthesis S right parenthesis end fraction equals x over 12$

(ii) Number of white balls in the box = x + 6 Total number of balls in the box = 12 + 6 = 18. i.e., n(S) = 18
Let B be the favourable outcomes of getting new white balls, then
n(B) = x + 6
Therefore,
P(B) = $fraction numerator straight n left parenthesis straight B right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals fraction numerator x plus 6 over denominator 18 end fraction$
Now according to question
P(B) = 2P(A)
$rightwards double arrow space space space space space space space space space space space space fraction numerator straight x plus 6 over denominator 18 end fraction equals 2 open parentheses x over 12 close parentheses rightwards double arrow space space space space space space space space space space space space fraction numerator x plus 6 over denominator 18 end fraction equals fraction numerator 2 x over denominator 12 end fraction rightwards double arrow space space space space space space space space space space space space space fraction numerator x plus 6 over denominator 18 end fraction equals fraction numerator 2 x over denominator 12 end fraction rightwards double arrow space space space space space space space space space space space space space fraction numerator x plus 6 over denominator 3 end fraction equals x over 6 rightwards double arrow space space space space space space space space space space space space space space fraction numerator x plus 6 over denominator 3 end fraction equals x space rightwards double arrow space space space space space space space space space space space space space 3 x space equals space x plus 6 rightwards double arrow space space space space space space space space space space space space space space 2 x space equals space 6 rightwards double arrow space space space space space space space space space space space space space space space x space equals space 3 space space space space space space space space space$
Hence, the number of white balls = 3.

For Daily Free Study Material Join wiredfaculty

Real Numbers

A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x.

Some More Questions From Real Numbers Chapter

Write the Sample Space when a coin is tossed.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location