There are 4 green, 2 purple, 1 orange and 5 yellow marbles in a pouch.…
2024
There are 4 green, 2 purple, 1 orange and 5 yellow marbles in a pouch. Shivansh chooses 1 marble at random, records colour & replaces it. He repeats this process 25 times. Which colour did Shivansh probably choose the greatest number of times?
Answer: D. Yellow — Concept: When an experiment such as drawing a marble at random with replacement is repeated many times, the outcome with the highest single-trial probability…
- A.
Green
- B.
Orange
- C.
Purple
- D.
Yellow
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Concept: When an experiment such as drawing a marble at random with replacement is repeated many times, the outcome with the highest single-trial probability is expected to occur most often overall, because expected frequency = probability × number of trials — a larger probability directly gives a larger expected count.
Total marbles in the pouch = 4 (green) + 2 (purple) + 1 (orange) + 5 (yellow) = 12.
Probability of drawing green on any trial = 4/12 = 1/3 ≈ 0.33.
Probability of drawing purple on any trial = 2/12 = 1/6 ≈ 0.17.
Probability of drawing orange on any trial = 1/12 ≈ 0.08.
Probability of drawing yellow on any trial = 5/12 ≈ 0.42.
Comparing the four probabilities: 5/12 (yellow) is the largest, followed by 4/12 (green), then 2/12 (purple), then 1/12 (orange).
Cross-check: Multiplying each probability by the 25 trials gives the expected number of times each colour would be drawn — yellow ≈ 25 × 5/12 ≈ 10.4 times, green ≈ 25 × 4/12 ≈ 8.3 times, purple ≈ 25 × 2/12 ≈ 4.2 times, and orange ≈ 25 × 1/12 ≈ 2.1 times. These expected counts sum to 25, matching the total number of trials, confirming the working is consistent.
Since yellow has both the highest single-trial probability and the highest expected count over the 25 trials, Shivansh most probably chose yellow the greatest number of times.