There are 3 red , 3 blue , 3 green marbles . What is probability that at least…
2023
There are 3 red , 3 blue , 3 green marbles . What is probability that at least two of them are of same color . If 3 marbles are done without replacement.
- A.
11/24
- B.
3/25
- C.
19/28
- D.
11/5
Attempted by 13 students.
Show answer & explanation
Correct answer: C
Answer: 19/28
Total possible outcomes: C(9,3) = 84.
Compute favourable outcomes:
Exactly two marbles of the same color and one of a different color: choose the color for the pair (3 ways) × C(3,2)=3 × choose 1 from the remaining 6 marbles = 6. So 3 × 3 × 6 = 54 ways.
All three marbles of the same color: choose the color (3 ways) × C(3,3)=1 → 3 × 1 = 3 ways.
Total favourable outcomes = 54 + 3 = 57.
Probability = 57/84 = (divide numerator and denominator by 3) = 19/28.