Difficulty: Easy
Correct Answer: 4/7
Explanation:
Introduction / Context:
This is a straightforward single draw probability question, testing understanding of the basic formula for probability in a simple situation. The aim is to compute the probability of drawing a white ball from a bag that contains both black and white balls.
Given Data / Assumptions:
Concept / Approach:
In the classical definition, probability of an event equals number of favourable outcomes divided by total number of possible outcomes, assuming all outcomes are equally likely. Here, favourable outcomes are white balls and total outcomes are all balls in the bag.
Step-by-Step Solution:
Total balls = 6 + 8 = 14.
Number of favourable outcomes (white balls) = 8.
Probability of drawing a white ball = favourable / total = 8 / 14.
Simplify 8 / 14 by dividing numerator and denominator by 2: 8 / 14 = 4 / 7.
Verification / Alternative check:
We can also compute the probability of drawing a black ball and then use complement. Probability of black = 6/14 = 3/7. Therefore probability of white = 1 - 3/7 = 4/7. This agrees with the direct counting method and confirms the result.
Why Other Options Are Wrong:
3/7 is the probability of drawing a black ball, not a white ball.
1/8 would be correct only if there were 8 balls total with 1 white, which is not the case.
3/4 would require 3 out of every 4 balls being white, that is 10.5 white balls out of 14, which is impossible.
Common Pitfalls:
The most common error is miscounting the total number of balls or mixing up the counts of black and white. Another minor mistake is forgetting to simplify the final fraction. Always identify clearly what outcomes are favourable and then divide by the total number of outcomes.
Final Answer:
Hence, the probability that the drawn ball is white is 4/7.
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