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A box contains 15 apples, out of which 5 are rotten. 4 apples are drawn from the box at random (one by one without replacement).
What is the probability that all 4 of them are rotten?
  • a)
    1/273
  • b)
    1/27
  • c)
    149/1365
  • d)
    3/233
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A box contains 15 apples, out of which 5 are rotten. 4 apples are draw...
Probability of drawing all 4 rotten apples:

Calculating the probability:
- The total number of ways to draw 4 apples out of 15 is 15C4.
- The number of ways to draw all 4 rotten apples out of 5 is 5C4.

Using the formula:
- Probability = (Number of favorable outcomes) / (Total number of outcomes)
- Probability = 5C4 / 15C4 = 1 / 273
Therefore, the probability that all 4 drawn apples are rotten is 1/273, which is option A.
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Community Answer
A box contains 15 apples, out of which 5 are rotten. 4 apples are draw...
Total number of apples in the box = 15
Number of ways of choosing 4 apples from these 15 apples = 15C4 = 15! / (4! × 11!) = (15×14×13×12) / (4×3×2) = 1365
Number of ways of choosing 4 rotten apples from 5 rotten apples = 5C4 = 5! / (4! × 1!) = 5
So, Required probability = 5/1365 = 1/273
Hence, option (a) is correct.
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