Pick a subset of {1, 2, · · · , 10} so that any subset is...

Pick a subset of {1, 2, · · · , 10} so that any subset is equally likely to be picked. What is the probability that

a. the subset contains the element one, given it is of size three?
b. the subset has no even numbers given that it is of size 4?
c. the maximum element of the subset is 8, given that the minimum element in it is 3?

Solutions

Expert Solution

Like {3}, {3, 4}, {3, 5}, ..

Also number of subsets where minimum is 3 and maximum is 8 is as subsets are formed using the numbers

{3, 4,5,6,7,8,9,10} with 3 and 8 fixed.

Like {3, 8}, {3, 4,8}, {3, 5,8},....

Hence the probability is

orchestra answered 1 year ago

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