There is a bag in which four balls with different weight are.
When I took one ball and took another ball out of this bag without putting the first one back, the second ball was heavier than the first one.
Find the probability that the second ball is heaviest in four ?
When I took one ball and took another ball out of this bag without putting the first one back, the second ball was heavier than the first one.
Find the probability that the second ball is heaviest in four ?
Answer
The number of the permutations to take out two of these four balls in order is 12 ways.
The number in case of the 2nd ball of them is heavier than the first one is half of 12 ways, it is 6 ways.
The number of the way that the second ball is the heaviest D is 3 ways of A-D, B-D and C-D.
Therefore the probability that the second ball is the heaviest among four balls is 3 / 6 = 1/2.
1/2
Solution
Suppose that light order in four balls is A, B, C, and D.
The number of the permutations to take out two of these four balls in order is 12 ways.
The number in case of the 2nd ball of them is heavier than the first one is half of 12 ways, it is 6 ways.
The number of the way that the second ball is the heaviest D is 3 ways of A-D, B-D and C-D.
Therefore the probability that the second ball is the heaviest among four balls is 3 / 6 = 1/2.
