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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
out in the box. the probability of drawing a black ball is now double of what it was
before. Find x.?
Most Upvoted Answer
A box contains 12 balls out of which x are black. if one ball is drawn...
Understanding the Problem
We have a box containing 12 balls, with x of them being black. We need to determine the value of x based on the probability conditions given.
Initial Probability Calculation
- The total number of balls = 12
- The number of black balls = x
- The probability of drawing a black ball (P1) is calculated as:
P1 = Number of black balls / Total number of balls
P1 = x / 12
Condition with Additional Black Balls
- When 6 more black balls are added, the total number of black balls becomes (x + 6).
- The new total number of balls in the box is now 18 (12 original + 6 new).
- The new probability of drawing a black ball (P2) is:
P2 = (x + 6) / 18
Setting Up the Equation
According to the problem, the new probability (P2) is double the initial probability (P1):
P2 = 2 * P1
Substituting the expressions we calculated:
(x + 6) / 18 = 2 * (x / 12)
Solving the Equation
1. Cross-multiply to eliminate the fractions:
(x + 6) * 12 = 2 * x * 18
2. This simplifies to:
12x + 72 = 36x
3. Rearranging gives:
36x - 12x = 72
24x = 72
4. Dividing both sides by 24:
x = 3
Final Conclusion
The value of x, the number of black balls initially in the box, is 3.
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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 out in the box. the probability of drawing a black ball is now double of what it was before. Find x.?
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