In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up…
2026
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 red nor green?
- A.
1/3
- B.
3/4
- C.
7/19
- D.
2/3
Attempted by 9 students.
Show answer & explanation
Correct answer: A
Concept: For equally likely outcomes, the probability of an event E is P(E) = n(E) / n(S), where n(S) is the total number of possible outcomes (the sample space) and n(E) is the number of outcomes favourable to E.
Total balls in the box (the sample space) = 8 red + 7 blue + 6 green = 21.
The event 'neither red nor green' is satisfied only by the blue balls, so the number of favourable outcomes = 7.
Applying the formula: P(neither red nor green) = 7 / 21 = 1/3.
Cross-check: The complementary event 'red or green' has (8 + 6) = 14 favourable outcomes, giving P(red or green) = 14/21 = 2/3. Since the two events partition the sample space, their probabilities must add to 1, and indeed 1/3 + 2/3 = 1, confirming the result.