Out of `30` consecutive integers `2` are chosen at random. The probability that their sum is odd, is

Options

A. a) `(14)/(29)`
B. b) `(16)/(29)`
C. c) `(15)/(29)`
D. d) `(10)/(29)`

Answer

c) `(15)/(29)`

Explanation

Total sample space `= 30_(C_2) = 435`


Sum is odd, if one of the integers is odd and the other is even.


`Odd+Even=Odd`


`Even+Odd=Odd`


Favourable cases `= (15_(C_1))^2=15*15=225`


In 30 consecutive integers, there are 15 odd and 15 even.


Required probability `= (225)/435`


`=15/29`


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