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 9th one examined is the last rotten one?
Answer: Option A
:
A
Lets consider upto the 9thapple. 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 = 4C3×11C515C3×17C1
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:
A
Lets consider upto the 9thapple. 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 = 4C3×11C515C3×17C1
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