A box contains 12 balls out of which x are black. If 6 more black balls are put in the box, the probability of drawing a black ball

Question

A box contains 12 balls out of which x are black. If 6 more black balls are put in the box, the probability of drawing a black ball

A box contains 12 balls out of which x are black. If 6 more black balls are put in the box, the probability of drawing a black ball now is double of what it was before. The value of x is ………

A) 5

B) 4

C) 3

D) 2

Monjur Alahi

8 views

2025-01-04 04:42

2 Answers

Salim Ahmed Kawsar

Correct option is: C) 3

8 views Answered 2023-02-05 15:29

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct option is: C) 3

Total balls is 12 in which x are black.

\(\therefore\) Probability of drawing a black ball = \(\frac x{12}\)

After putting 6 more black balls.

Total balls = 12 + 6 = 18

and total black balls = x + 6

\(\therefore\) Probability of drawing a black balls after putting 6 more black balls = \(\frac {x+6}{18}\)

According to given conditions, we have

\(\frac {x+6}{18}\) = \(\frac {2x}{12}\)

\(\Rightarrow\) 12 (x + 6) = 36x (By cross multiplication)

\(\Rightarrow\) 12x + 72 = 36x

\(\Rightarrow\) 36x -12x = 72

\(\Rightarrow\) 24x = 72

\(\Rightarrow\) x = \(\frac {72}{24}= 3\)

Hence, the value of x is 3.