A bag contains 8 red flowers, 7 blue flowers and 6 green flowers. If one flower is picked at random, what is the probability that the chosen flower is neither red nor green (that is, it is blue)?

Introduction / Context:
This problem tests basic probability concepts in a simple selection setting. We have a mixture of differently coloured flowers in a bag and we pick one flower at random. The goal is to find the probability that the flower is neither red nor green, which effectively means we want the probability that the flower is blue.

Given Data / Assumptions:

• Number of red flowers = 8.
• Number of blue flowers = 7.
• Number of green flowers = 6.
• One flower is selected at random.
• Each flower is equally likely to be selected.

Concept / Approach:
Probability of an event is defined as: favorable outcomes divided by total possible outcomes, provided all outcomes are equally likely. Here the favorable event is choosing a blue flower, because blue is the only colour that is neither red nor green.

Step-by-Step Solution:
Step 1: Compute the total number of flowers. Total flowers = 8 red + 7 blue + 6 green = 21 flowers. Step 2: Identify the favourable outcomes. The flower must be neither red nor green, so it must be blue, and there are 7 blue flowers. Step 3: Use the probability formula. Probability = favourable outcomes / total outcomes = 7 / 21. Step 4: Simplify the fraction 7 / 21 by dividing numerator and denominator by 7. Probability = 1 / 3.

Verification / Alternative check:
As a quick check, the probability of picking red is 8 / 21 and of picking green is 6 / 21. The probability of red or green is (8 + 6) / 21 = 14 / 21 = 2 / 3. Therefore, the probability of not red and not green is 1 minus 2 / 3 which is 1 / 3, confirming the result.

Why Other Options Are Wrong:
7/20 and 3/7 use incorrect denominators or numerators that do not match the total counts. 2/3 corresponds to picking red or green, which is the complement event rather than the desired one.

Common Pitfalls:
A common mistake is to forget to include all flower types when computing the total or to misinterpret the phrase neither red nor green. Another error is to subtract probabilities incorrectly instead of using the direct count of blue flowers.

Final Answer:
The probability that the randomly selected flower is neither red nor green is 1/3.