An urn contains 6 red, 4 blue, 2 green and 3 yellow marbles. If four marbles…
2023
An urn contains 6 red, 4 blue, 2 green and 3 yellow marbles. If four marbles are picked at random, what is the probability that at least one is blue ?
- A.
4/15
- B.
1/35
- C.
69/91
- D.
4/105
Attempted by 3 students.
Show answer & explanation
Correct answer: C
Total marbles = 6 red + 4 blue + 2 green + 3 yellow = 15. We pick 4 marbles.
Strategy: Use the complement (1 − probability of no blue).
Total number of ways to choose any 4 marbles = C(15,4) = 1365.
Number of ways with no blue marbles: choose 4 from the 11 non-blue marbles (6 red + 2 green + 3 yellow) = C(11,4) = 330.
Probability of no blue = 330 / 1365 = 22/91.
Probability of at least one blue = 1 - 22/91 = 69/91.
Final answer: 69/91