A bag contains 6 black balls and 8 white balls. One ball is drawn at random from the bag. What is the probability that the ball drawn is white?

Introduction / Context:
This is a basic probability question involving a single draw from a collection of balls of two colours. The task is to compute the chance that the ball drawn at random from the bag is white. Problems of this type give good practice with the fundamental formula for probability based on equally likely outcomes.

Given Data / Assumptions:

• Number of black balls = 6.
• Number of white balls = 8.
• Total number of balls in the bag = 6 + 8 = 14.
• One ball is drawn at random, and each ball is equally likely to be selected.
• The event of interest is that the selected ball is white.

Concept / Approach:
In a simple uniform sample space, the probability of an event is equal to the ratio of favourable outcomes to total possible outcomes. Here, each ball is considered one outcome. Favourable outcomes correspond to the white balls. We do not need combinations because only one ball is drawn, and order is not an issue.

Step-by-Step Solution:
Compute total number of balls: 6 + 8 = 14. Number of favourable balls (white) = 8. Probability of drawing a white ball = favourable outcomes / total outcomes. So required probability = 8 / 14. Simplify 8 / 14 by dividing numerator and denominator by 2 to obtain 4 / 7.

Verification / Alternative check:
We can also compute the probability of drawing a black ball and then use the complement. Probability of black ball = 6 / 14 = 3 / 7. Therefore probability of white ball = 1 minus 3 / 7 = 4 / 7. This second method arrives at the same fraction and gives a quick consistency check for the calculation.

Why Other Options Are Wrong:
3/7 is the probability of drawing a black ball, not a white ball. 1/8 would correspond to 1 white ball out of 8 total balls, which does not match the situation. 3/4 suggests that three quarters of all balls are white, which would require 10.5 white balls out of 14, which is impossible.

Common Pitfalls:
The most common error is mixing up the counts of black and white balls or forgetting to add them correctly when finding the total. Another mistake is to leave the fraction unsimplified, although in probability questions it is usually better to present the answer in simplest form. Always identify the number of favourable cases clearly before forming the ratio.

Final Answer:
The probability that the ball drawn from the bag is white is 4/7.