In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up…
2025
In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?
- A.
2/3
- B.
8/21
- C.
4/32
- D.
5/6
Show answer & explanation
Correct answer: B
Concept: For equally likely outcomes, the classical probability of an event E is P(E) = (number of favorable outcomes) / (total number of outcomes). When a sample space is partitioned into mutually exclusive categories (here: red, blue, and green balls), the event 'neither of two categories' is exactly the remaining category.
Total balls in the box = red + blue + green = 8 + 7 + 6 = 21.
Since every ball is exactly one of red, blue, or green, the event 'neither blue nor green' consists of only the red balls.
Number of favorable outcomes (red balls) = 8.
Probability = favorable outcomes / total outcomes = 8/21.
Check: adding the probabilities of all three colours should give 1 - P(red) + P(blue) + P(green) = 8/21 + 7/21 + 6/21 = 21/21 = 1, confirming the total is correctly accounted for.