Question

4 out of 15 apples are rotten. They are taken out one by one at random and examined. The ones which are examined are not replaced. What is the probability that the 9^th one examined is the last rotten one?

• A.
• B.
• C.
• D. none of these

Answer 1

The correct option is A

option (a)

Lets consider upto the 9^th apple. The first 8 apples should have 3 rotten ones and remaining 5 good ones. This can be chosen in ⁴C₃ × ¹¹C₅ ways. Total number of selections of 8 apples out of 15 apples is ¹⁵C₈. The last apple is the only rotten one left, which can be selected in 1 way. Total number of ways of selecting that 1 apple from remaining 15 – 8 = 7 apples = ⁷C₁ ways

Total probability =